Question

A builder set up a wooden frame in which to pour concrete for a foundation to a house. The length of the wooden frame is 24 feet. The width is 32 feet. The diagonal is 40 feet. Which best describes the foundation?
The foundation cannot be a rectangle: 24 + 32 not-equals 40.
The foundation cannot be a rectangle: (24 + 32) squared not-equals 40 squared.
The foundation cannot be a rectangle: StartRoot 24 squared + 23 squared EndRoot not-equals 40 squared.
The foundation may be a rectangle: 24 squared + 32 squared = 40 squared.

Answer 1

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The answer is the last option, which is: The foundation may be a rectangle: ${24}^2 + {32}^2 = {40}^2$

The explanation for this problem is shown below:

1- A rectangle is defined as a parallelogram whose opposite sides are parallel and congruent. Its interior angles are right angles.

2- Keeping the definition above on mind, the diagonal of a rectangle divides it into to right triangles. So, we can verify if the shape of the frame is a rectangle by using the Pythagorean Theorem, which is:

$=> a^{2}= b^{2} +c^{2}$

Where aa is the hypotenuse (the measure of the diagonal) and bb and cc are the other sides of the right triangle.

3- Therefore, you have that aa must be equal to 40 to conclude that it is a rectangle:

Answer 2

A rectangle is defined as a parallelogram whose opposite sides are parallel and congruent. Its interior angles are right angles.

2- Keeping the definition above on mind, the diagonal of a rectangle divides it into to right triangles. So, we can verify if the shape of the frame is a rectangle by using the Pythagorean Theorem, which is:

=> a^{2}= b^{2} +c^{2}=>a2=b2+c2

Where aa is the hypotenuse (the measure of the diagonal) and bb and cc are the other sides of the right triangle.

3- Therefore, you have that aa must be equal to 40 to conclude that it is a rectangle