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, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a rectangular prism with dimensions of 44 in (length), 24 in (width), and 14 in (height). The diagonal will be the hypotenuse of a right triangle formed by two of the sides.
Let's calculate the diagonal for the length and width of the coffee table:
For the length and width:
diagonal = √(length^2 + width^2)
diagonal = √(44^2 + 24^2)
diagonal = √(1936 + 576)
diagonal = √(2512)
diagonal ≈ 50.12 in
Now, let's calculate the diagonal for the height and width:
For the height and width:
diagonal = √(height^2 + width^2)
diagonal = √(14^2 + 24^2)
diagonal = √(196 + 576)
diagonal = √(772)
diagonal ≈ 27.8 in
Keysha should make each diagonal approximately 50.1 inches for the length and width, and 27.8 inches for the height and width.