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 of a rectangular prism can be found by finding the square root of the sum of the squares of its dimensions.
Let's denote the length as L, the width as W, and the height as H.
The length of each diagonal can be found using the formula:
Diagonal = √(L^2 + W^2 + H^2)
For this coffee table, the length (L) is 44 inches, the width (W) is 24 inches, and the height (H) is 14 inches.
Plugging these values into the formula, we get:
Diagonal = √(44^2 + 24^2 + 14^2)
= √(1936 + 576 + 196)
= √(2708)
≈ 52.1 inches
Therefore, Keysha should make each diagonal approximately 52.1 inches long.