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 24in., 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 the length, width, and height of the rectangular prism be represented by the variables l, w, and h respectively.
The diagonal can be thought of as the hypotenuse of a right triangle, with the length and width as the legs.
Using the Pythagorean theorem, we have:
diagonal = sqrt((length)^2 + (width)^2)
diagonal = sqrt((44in)^2 + (24in)^2)
diagonal = sqrt(1936in^2 + 576in^2)
diagonal = sqrt(2512in^2)
diagonal ≈ 50.1in
Therefore, Keysha should make each diagonal approximately 50.1 inches long.