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.
Let's label the length, width, and height as follows:
Length = l = 44 in
Width = w = 24 in
Height = h = 14 in
We can find the diagonal on the bottom face of the rectangular prism using the formula:
Diagonal = √(length^2 + width^2)
Diagonal = √(44^2 + 24^2)
= √(1936 + 576)
= √(2512)
≈ 50.1 in
Now, we can find the diagonal running from one bottom corner to the top opposite corner of the rectangular prism.
This diagonal can be found using the formula:
Diagonal = √(length^2 + width^2 + height^2)
Diagonal = √(44^2 + 24^2 + 14^2)
= √(1936 + 576 + 196)
= √(2708)
≈ 52 in
So, the length of each diagonal should be 50.1 inches and 52 inches, respectively.