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 45 in., the width 24 in., and the height 13 in. Find the length Keysha should make each diagonal. Round the answer to the nearest tenth.
To find the length of the diagonal, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by two sides of the rectangle.
Let's consider the diagonal that goes from one corner of the table to the opposite corner along the length. This diagonal will form a right triangle with the length of the table (45 inches) as one side and the height of the table (13 inches) as the other side. We can find the length of this diagonal using the Pythagorean theorem:
diagonal^2 = length^2 + height^2
diagonal^2 = 45^2 + 13^2
diagonal^2 = 2025 + 169
diagonal^2 = 2194
diagonal ≈ √2194
diagonal ≈ 46.8 inches
Now, let's consider the diagonal that goes from one corner of the table to the opposite corner along the width. This diagonal will form a right triangle with the width of the table (24 inches) as one side and the height of the table (13 inches) as the other side. We can find the length of this diagonal using the Pythagorean theorem:
diagonal^2 = width^2 + height^2
diagonal^2 = 24^2 + 13^2
diagonal^2 = 576 + 169
diagonal^2 = 745
diagonal ≈ √745
diagonal ≈ 27.3 inches
Therefore, Keysha should make each diagonal approximately 46.8 inches and 27.3 inches long.