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)
in.
To find the length of each diagonal, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Since we want to find the length of each diagonal, we can imagine a right triangle within the rectangular prism. The diagonals will be the hypotenuses of these triangles.
We can solve for the length of each diagonal using the following formula:
diagonal = √(length^2 + width^2 + height^2)
Plugging in the given values:
diagonal = √(44^2 + 24^2 + 14^2)
diagonal = √(1936 + 576 + 196)
diagonal = √(2708)
diagonal ≈ 52.0 in.
Therefore, Keysha should make each diagonal approximately 52.0 inches long.
To find the length of each diagonal, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal is the hypotenuse, and the other two sides are the length and width of the coffee table.
Let's calculate it step by step:
Step 1: Square the length and width:
Length^2 = 44^2 = 1936 in^2
Width^2 = 24^2 = 576 in^2
Step 2: Find the sum of the squares:
1936 + 576 = 2512 in^2
Step 3: Take the square root of the sum:
√(2512) ≈ 50.12 in.
Therefore, Keysha should make each diagonal approximately 50.12 inches long.
To find the length of each diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, each diagonal forms a right triangle with two sides being the length and width of the coffee table, and the diagonal being the hypotenuse.
Let's calculate the length of each diagonal step by step:
1. Square the length: 44^2 = 1936
2. Square the width: 24^2 = 576
3. Sum the squares: 1936 + 576 = 2512
4. Take the square root of the sum: sqrt(2512) ≈ 50.12
So, Keysha should make each diagonal approximately 50.1 inches long.