Keysha is building a coffee table, its 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 your answer to the nearest tenth.
To find the length of each diagonal, we will use the Pythagorean theorem.
First, let's find the diagonal for the length and the width.
The diagonal for the length and width is the hypotenuse of a right triangle with legs equal to the length and the width of the coffee table.
Using the Pythagorean theorem:
diagonal_length_width = √(44^2 + 24^2) = √(1936 + 576) = √2512 ≈ 50.1 in
Next, let's find the diagonal for the length and the height.
The diagonal for the length and height is the hypotenuse of a right triangle with legs equal to the length and the height of the coffee table.
Using the Pythagorean theorem:
diagonal_length_height = √(44^2 + 14^2) = √(1936 + 196) = √2132 ≈ 46.1 in
Finally, let's find the diagonal for the width and the height.
The diagonal for the width and height is the hypotenuse of a right triangle with legs equal to the width and the height of the coffee table.
Using the Pythagorean theorem:
diagonal_width_height = √(24^2 + 14^2) = √(576 + 196) = √772 ≈ 27.8 in
Therefore, Keysha should make each diagonal approximately 50.1 in, 46.1 in, and 27.8 in long for the length and width, length and height, and width and height diagonals, respectively.