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
To find the length of each diagonal, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse (diagonal) is the metal diagonal, and the other two sides are the length and width (or height).
So, let's calculate the length of each diagonal.
1) Diagonal 1: Length and width
Using the Pythagorean theorem, we have:
Length of diagonal 1 = √(Length^2 + Width^2)
= √(44^2 + 24^2)
= √(1936 + 576)
= √(2512)
≈ 50.1 inches (rounded to the nearest tenth)
2) Diagonal 2: Length and height
Using the Pythagorean theorem, we have:
Length of diagonal 2 = √(Length^2 + Height^2)
= √(44^2 + 14^2)
= √(1936 + 196)
= √(2132)
≈ 46.2 inches (rounded to the nearest tenth)
3) Diagonal 3: Width and height
Using the Pythagorean theorem, we have:
Length of diagonal 3 = √(Width^2 + Height^2)
= √(24^2 + 14^2)
= √(576 + 196)
= √(772)
≈ 27.8 inches (rounded to the nearest tenth)
Therefore, Keysha should make each diagonal approximately 50.1 inches, 46.2 inches, and 27.8 inches in length, rounded to the nearest tenth.