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)
To find the length of each diagonal, we can use the Pythagorean theorem.
Let's label the length, width, and height as follows:
Length (l) = 44 in.
Width (w) = 24 in.
Height (h) = 14 in.
To find the diagonal, we can create a right triangle with one side as the length of the coffee table, one side as the width of the coffee table, and the diagonal as the hypotenuse.
Using the Pythagorean theorem:
diagonal^2 = l^2 + w^2 + h^2
diagonal^2 = 44^2 + 24^2 + 14^2
diagonal^2 = 1936 + 576 + 196
diagonal^2 = 2708
Taking the square root of both sides:
diagonal ≈ √2708
diagonal ≈ 52.0 in.
Therefore, Keysha should make each diagonal approximately 52.0 inches long.