Keysha is building a coffee table. It’s going to be in the shape of a rectangular prism, without the faces. She wants to make the table decorative by adding metal diagonals. The length of the coffee table will be 44 in., the width 24 in., and the height 14 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.(1 point)

Answer 1

To find the length of each diagonal, we need to find the length of the diagonal of each face of the rectangular prism.

For the length face, the diagonal is the hypotenuse of a right triangle with legs 24 in. and 14 in. We can use the Pythagorean theorem to find the length.

So, the length of the diagonal of the length face is √(24^2 + 14^2) = √(576 + 196) = √772 ≈ 27.8 in.

For the width face, the diagonal is the hypotenuse of a right triangle with legs 44 in. and 14 in. We can use the Pythagorean theorem to find the length.

So, the length of the diagonal of the width face is √(44^2 + 14^2) = √(1936 + 196) = √2132 ≈ 46.1 in.

For the height face, the diagonal is the hypotenuse of a right triangle with legs 44 in. and 24 in. We can use the Pythagorean theorem to find the length.

So, the length of the diagonal of the height face is √(44^2 + 24^2) = √(1936 + 576) = √2512 ≈ 50.1 in.

Therefore, the length Keysha should make each diagonal is approximately 27.8 in. for the length face, 46.1 in. for the width face, and 50.1 in. for the height face.

Answer 2

Explain a proof of the Pythagorean Theorem