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*15. Here is an old-fashioned way to make a rectangu- lar foundation for a house. Take a pair of identical pieces of wood for the length of the house and another pair of identical pieces of wood for the width of the house. Place the wood on the ground to show approximately where the foundation will go. The pieces of wood now form a quadrilateral whose opposite sides are the same length. Measure the two diagonals of the quadrilateral, and keep adjusting the quadrilateral until the two diagonals are the same length. Explain why the quadrilateral must now be a rectangle. In other words, explain why the quadrilateral must have 4 right angles.

*15. Here is an old-fashioned way to make a rectangu- lar foundation for a house. Take a pair of identical pieces of wood for the length of the house and another pair of identical pieces of wood for the width of the house. Place the wood on the ground to show approximately where the foundation will go. The pieces of wood now form a quadrilateral whose opposite sides are the same length. Measure the two diagonals of the quadrilateral, and keep adjusting the quadrilateral until the two diagonals are the same length. Explain why the quadrilateral must now be a rectangle. In other words, explain why the quadrilateral must have 4 right angles.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### How to Make a Rectangular Foundation for a House: An Old-Fashioned Method #### Step-by-Step Guide 1. **Materials Needed**: - Two pairs of identical pieces of wood - One pair for the length of the house - Another pair for the width of the house 2. **Setup**: - Place the wood on the ground to mark where the foundation will be located. - Arrange the pieces of wood to form a quadrilateral. At this point, ensure that the opposite sides of the quadrilateral are of equal length. 3. **Measuring and Adjusting**: - Measure the two diagonals of the quadrilateral. - Adjust the arrangement of the quadrilateral until the two diagonals are of equal length. 4. **Explanation**: At this point, the quadrilateral must now be a rectangle. This is because in any quadrilateral with both pairs of opposite sides equal in length, having equal diagonals is a unique property of rectangles. The equal diagonals ensure that each angle is 90 degrees, thereby forming a rectangle. #### Why the Quadrilateral Must Have Four Right Angles In other words, by ensuring that your diagonals are equal while maintaining the lengths of the opposite sides equal, you enforce the condition that all angles in the quadrilateral are right angles (90 degrees). This results in a perfect rectangular shape for the foundation. *Diagram Explanation (not shown here)*: - Imagine a simple quadrilateral with four sides. - Observe how adjusting the sides ensures both diagonals become equal. - Visualize how the angles adjust to become right angles accordingly, verifying the shape as a rectangle. This method provides a practical and reliable way to ensure your house foundation has the proper rectangular shape without requiring advanced tools.
Transcribed Image Text:### How to Make a Rectangular Foundation for a House: An Old-Fashioned Method #### Step-by-Step Guide 1. **Materials Needed**: - Two pairs of identical pieces of wood - One pair for the length of the house - Another pair for the width of the house 2. **Setup**: - Place the wood on the ground to mark where the foundation will be located. - Arrange the pieces of wood to form a quadrilateral. At this point, ensure that the opposite sides of the quadrilateral are of equal length. 3. **Measuring and Adjusting**: - Measure the two diagonals of the quadrilateral. - Adjust the arrangement of the quadrilateral until the two diagonals are of equal length. 4. **Explanation**: At this point, the quadrilateral must now be a rectangle. This is because in any quadrilateral with both pairs of opposite sides equal in length, having equal diagonals is a unique property of rectangles. The equal diagonals ensure that each angle is 90 degrees, thereby forming a rectangle. #### Why the Quadrilateral Must Have Four Right Angles In other words, by ensuring that your diagonals are equal while maintaining the lengths of the opposite sides equal, you enforce the condition that all angles in the quadrilateral are right angles (90 degrees). This results in a perfect rectangular shape for the foundation. *Diagram Explanation (not shown here)*: - Imagine a simple quadrilateral with four sides. - Observe how adjusting the sides ensures both diagonals become equal. - Visualize how the angles adjust to become right angles accordingly, verifying the shape as a rectangle. This method provides a practical and reliable way to ensure your house foundation has the proper rectangular shape without requiring advanced tools.
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