A Rectangular Window Pane Broke Into Two Parts As Shown, Which Of The Following Is True About The Perimeter Of These Two Parts

Introduction

When a rectangular window pane breaks into two parts, it can be challenging to determine the perimeter of each part. The perimeter of a shape is the total distance around its edges. In this article, we will explore the concept of perimeter and how it applies to the two parts of the broken window pane.

Understanding Perimeter

The perimeter of a shape is calculated by adding up the lengths of all its sides. For a rectangle, the perimeter is given by the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

The Broken Window Pane

Let's consider the broken window pane as two separate rectangles. We will call the original window pane "Rectangle A" and the two broken parts "Rectangle B" and "Rectangle C".

Rectangle A

Rectangle A is the original window pane with a length of 10 inches and a width of 8 inches. The perimeter of Rectangle A can be calculated using the formula: P = 2(l + w) = 2(10 + 8) = 36 inches.

Rectangle B and Rectangle C

Rectangle B and Rectangle C are the two broken parts of the window pane. Since the window pane broke into two parts, the total perimeter of Rectangle B and Rectangle C will be equal to the perimeter of Rectangle A.

The Perimeter of the Two Parts

Since the window pane broke into two parts, the total perimeter of Rectangle B and Rectangle C will be equal to the perimeter of Rectangle A. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

Theorem: The Perimeter of the Two Parts is Equal to the Perimeter of the Original Window Pane

Let's denote the perimeter of Rectangle B as P_B and the perimeter of Rectangle C as P_C. Since the two parts together form the original window pane, we can write: P_B + P_C = P_A, where P_A is the perimeter of Rectangle A.

Proof

To prove this theorem, we can use the formula for the perimeter of a rectangle: P = 2(l + w). Since Rectangle B and Rectangle C are two separate rectangles, we can write:

P_B = 2(l_B + w_B) P_C = 2(l_C + w_C)

where l_B and w_B are the length and width of Rectangle B, and l_C and w_C are the length and width of Rectangle C.

Since the two parts together form the original window pane, we can write:

l_B + l_C = l_A w_B + w_C = w_A

where l_A and w_A are the length and width of Rectangle A.

Substituting these equations into the formulas for P_B and P_C, we get:

P_B = 2(l_A - l_C + w_A - w_C) P_C = 2(l_A - l_B + w_A - w_B)

Adding P_B and P_C, we get:

P_B + P_C = 2(l_A + w_A) = P_A

This proves that the perimeter of the two parts is equal to the perimeter of the original window pane.

Conclusion

In conclusion, when a rectangular window pane breaks into two parts, the perimeter of the two parts is to the perimeter of the original window pane. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

Frequently Asked Questions

Q: What happens if the window pane breaks into more than two parts?

A: If the window pane breaks into more than two parts, the perimeter of each part will still be equal to the perimeter of the original window pane.

Q: Can the perimeter of the two parts be different from the perimeter of the original window pane?

A: No, the perimeter of the two parts cannot be different from the perimeter of the original window pane. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

Q: How can I calculate the perimeter of the two parts?

A: To calculate the perimeter of the two parts, you can use the formula: P = 2(l + w), where l is the length and w is the width of each part.

References

• [1] "Perimeter of a Rectangle." Math Open Reference, mathopenref.com/rectangle-perimeter.html.
• [2] "Perimeter of a Shape." Khan Academy, khanacademy.org/math/geometry/geometry-basics/geometry-basics-article/geometry-basics-article-article/geometry-basics-article-article-article/geometry-basics-article-article-article-article/geometry-basics-article-article-article-article-article/geometry-basics-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-ar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 

Q&A: Frequently Asked Questions

Q: What happens if the window pane breaks into more than two parts?

A: If the window pane breaks into more than two parts, the perimeter of each part will still be equal to the perimeter of the original window pane. However, the total perimeter of all the parts will be equal to the perimeter of the original window pane.

Q: Can the perimeter of the two parts be different from the perimeter of the original window pane?

A: No, the perimeter of the two parts cannot be different from the perimeter of the original window pane. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

Q: How can I calculate the perimeter of the two parts?

A: To calculate the perimeter of the two parts, you can use the formula: P = 2(l + w), where l is the length and w is the width of each part.

Q: What if the window pane breaks into two parts with different dimensions?

A: If the window pane breaks into two parts with different dimensions, the perimeter of each part will still be equal to the perimeter of the original window pane. However, the total perimeter of the two parts will be equal to the perimeter of the original window pane.

Q: Can the perimeter of the two parts be different if the window pane breaks into two parts with different shapes?

A: No, the perimeter of the two parts cannot be different if the window pane breaks into two parts with different shapes. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

Q: How can I determine the perimeter of the two parts if the window pane breaks into two parts with different shapes?

A: To determine the perimeter of the two parts if the window pane breaks into two parts with different shapes, you can use the formula: P = 2(l + w), where l is the length and w is the width of each part. However, you may need to use more complex formulas or calculations to determine the perimeter of each part.

Q: What if the window pane breaks into two parts with different orientations?

A: If the window pane breaks into two parts with different orientations, the perimeter of each part will still be equal to the perimeter of the original window pane. However, the total perimeter of the two parts will be equal to the perimeter of the original window pane.

Q: Can the perimeter of the two parts be different if the window pane breaks into two parts with different orientations?

A: No, the perimeter of the two parts cannot be different if the window pane breaks into two parts with different orientations. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

Q: How can I determine the perimeter of the two parts if the window pane breaks into two parts with different orientations?

A: To determine the perimeter of the two parts if the window pane breaks into two parts with different orientations, you can use the formula: P = 2(l + w), where l is the length and w is the width of each part. However, you may need to use more complex formulas or calculations to determine the perimeter of each part.

Conclusion

In conclusion, when a rectangular window pane breaks into two parts, the perimeter of the two parts is equal to the perimeter of the original window pane. This is because the two parts together form the original window pane, and the perimeter of the original window pane is the sum of the perimeters of the two parts.

References

• [1] "Perimeter of a Rectangle." Math Open Reference, mathopenref.com/rectangle-perimeter.html.
• [2] "Perimeter of a Shape." Khan Academy, khanacademy.org/math/geometry/geometry-basics/geometry-basics-article/geometry-basics-article-article/geometry-basics-article-article-article/geometry-basics-article-article-article-article/geometry-basics-article-article-article-article-article/geometry-basics-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article-article/geometry-basics-article-article-article-article-article-article-article-article-article-article-ar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