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?

Answer 1

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 $a$ is the hypotenuse (the measure of the diagonal) and $b$ and $c$ are the other sides of the right triangle.

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

$\\a=\sqrt{24^{2}+32^{2}} \\ a=40$

4-So, as you can see, the answer is the option mentioned before.

Answer 2

Answer:

The correct answer is attached below!