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 point)
To find the length of each diagonal, we need to calculate the length of the metal diagonals that will be added to the coffee table. The metal diagonals will form a right triangle with the length, width, and height of the table as the sides.
We can use the Pythagorean theorem to find the length of the diagonal. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
In this case, the length of the table is the longest side, so we need to find the length of the hypotenuse.
Let's label the length, width, and height of the table as follows:
Length of the table (l) = 44 in.
Width of the table (w) = 24 in.
Height of the table (h) = 14 in.
Using the Pythagorean theorem, we have:
diagonal = √(l^2 + w^2 + h^2)
Substituting the given values:
diagonal = √(44^2 + 24^2 + 14^2)
Calculating the square of each term:
diagonal = √(1936 + 576 + 196)
Adding the terms inside the square root:
diagonal = √(2708)
Taking the square root of 2708:
diagonal = 52.06
Rounding the answer to the nearest tenth:
diagonal ≈ 52.1 inches
Therefore, Keysha should make each diagonal approximately 52.1 inches long.
To find the length of each diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the two other sides.
Let's consider one diagonal as the hypotenuse of a right triangle, and the other two sides as the lengths and height of the coffee table.
Using the formula, we have:
Diagonal^2 = Length^2 + Width^2 + Height^2
Substituting the given values, we get:
Diagonal^2 = 44^2 + 24^2 + 14^2
Diagonal^2 = 1936 + 576 + 196
Diagonal^2 = 2708
To find the diagonal, we take the square root of both sides:
Diagonal = √2708
Using a calculator, we find:
Diagonal ≈ 52.1 inches
Therefore, Keysha should make each diagonal approximately 52.1 inches long.
To find the length of each diagonal, we need to find the length of the diagonal of each face of the rectangular prism.
For the length face, the diagonal is the hypotenuse of a right triangle with legs 24 in. and 14 in. We can use the Pythagorean theorem to find the length.
So, the length of the diagonal of the length face is √(24^2 + 14^2) = √(576 + 196) = √772 ≈ 27.8 in.
For the width face, the diagonal is the hypotenuse of a right triangle with legs 44 in. and 14 in. We can use the Pythagorean theorem to find the length.
So, the length of the diagonal of the width face is √(44^2 + 14^2) = √(1936 + 196) = √2132 ≈ 46.1 in.
For the height face, the diagonal is the hypotenuse of a right triangle with legs 44 in. and 24 in. We can use the Pythagorean theorem to find the length.
So, the length of the diagonal of the height face is √(44^2 + 24^2) = √(1936 + 576) = √2512 ≈ 50.1 in.
Therefore, the length Keysha should make each diagonal is approximately 27.8 in. for the length face, 46.1 in. for the width face, and 50.1 in. for the height face.