To find the length of each diagonal, we can use the Pythagorean theorem.
The diagonal will be the hypotenuse of a right triangle, with one leg being the height of the coffee table (14 in) and the other leg being the hypotenuse of a right triangle in the base of the coffee table.
To find the hypotenuse of the base right triangle, we can use the Pythagorean theorem again.
The base right triangle has one leg measuring 24 in and the other leg measuring 44 in.
Using the Pythagorean theorem, we have:
base_hypotenuse^2 = (24 in)^2 + (44 in)^2
base_hypotenuse^2 = 576 in^2 + 1936 in^2
base_hypotenuse^2 = 2512 in^2
base_hypotenuse = √2512 in
base_hypotenuse ≈ 50.1 in
Now, we can find the diagonal by using the Pythagorean theorem for the second time:
diagonal^2 = (50.1 in)^2 + (14 in)^2
diagonal^2 = 2510.01 in^2 + 196 in^2
diagonal^2 = 2706.01 in^2
diagonal ≈ √2706.01 in
diagonal ≈ 52 in
Therefore, Keysha should make each diagonal approximately 52 inches long.
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 answer
1 answer