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≠40

The foundation cannot be a rectangle: (24+32)^2≠40^2

The foundation cannot be a rectangle: √24^2+32^2≠40^2

The foundation may be a rectangle: 24^2+32^2=40

^2

Answer 1

I have drawn a figure for the foundation of a frame with dimension 24 x 32 and diagonal.

For triangle ABD, if it's satisfy the Pythagorean theorem then ABCD will be a recatngle.

Pythagorean formula is:

a² + b² = c²

Where c is the hypotenuse and a, b are the legs of the triangle.

From triangle ABD:

AB² +BD² = AD²

24² + 32² = 40²

576 + 1024 = 1600 Simplify each sides separately.

1600 = 1600

From above result , 1600 = 1600 is true.

So, ABD is a right triangle, similarly ACD will also be right triangle.

Hence, ∠B and ∠C are right triangles.

So, ABCD is a rectangle.

Hence, the last choice is correct.

Hope this helps you!.

Answer 2

Answer:

D. The foundation may be a rectangle: 24^2 + 32^2 = 40^2

Step-by-step explanation:

I just took the quiz on edge