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
To find the length of each diagonal, we can use the Pythagorean theorem. The diagonal can be thought of as the hypotenuse of a right triangle formed by the length, width, and height of the coffee table.
Let’s label the length as L, the width as W, and the height as H. We have L = 44 in, W = 24 in, and H = 14 in.
Using the Pythagorean theorem, we have:
L² + W² = diagonal²
Substituting the given values, we have:
44² + 24² = diagonal²
1936 + 576 = diagonal²
2512 = diagonal²
To find the length of the diagonal, we take the square root of both sides:
diagonal = √2512
diagonal ≈ 50.1
Therefore, Keysha should make each diagonal approximately 50.1 inches long.