Keisha 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 inches the width 24 inches and the height 14 inches find the length Keisha should make each diagonal around the answer to the nearest tenth
To find the length of each diagonal, we can use the Pythagorean theorem.
Let's consider one of the diagonals that goes from one corner of the rectangular prism to the opposite corner.
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2 + height^2
Plugging in the values, we get:
diagonal^2 = 44^2 + 24^2 + 14^2
diagonal^2 = 1936 + 576 + 196
diagonal^2 = 2708
Taking the square root of both sides, we find:
diagonal = √2708
diagonal ≈ 52.03 inches
Therefore, Keisha should make each diagonal around 52.03 inches in length (to the nearest tenth).
To find the length of each diagonal, we can use the Pythagorean theorem, which states that in a right-angled 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 diagonal acts as the hypotenuse, and the sides of the rectangle act as the other two sides.
Let's label the length of the coffee table as "l", the width as "w", and the height as "h".
We are given:
l = 44 inches,
w = 24 inches, and
h = 14 inches.
To find the length of each diagonal, we need to calculate the diagonal for each face of the table.
1. Diagonal between the length and height:
Using the Pythagorean theorem, the diagonal (D1) can be found as follows:
D1^2 = l^2 + h^2
D1^2 = 44^2 + 14^2
D1^2 = 1936 + 196
D1^2 = 2132
D1 ≈ √2132
D1 ≈ 46.2 inches (rounded to the nearest tenth)
2. Diagonal between the width and height:
Using the Pythagorean theorem, the diagonal (D2) can be found as follows:
D2^2 = w^2 + h^2
D2^2 = 24^2 + 14^2
D2^2 = 576 + 196
D2^2 = 772
D2 ≈ √772
D2 ≈ 27.8 inches (rounded to the nearest tenth)
Therefore, the length of each diagonal is approximately:
D1 ≈ 46.2 inches
D2 ≈ 27.8 inches
To find the length of each diagonal, we can use the Pythagorean theorem since we have a rectangular prism (a rectangular shape).
First, let's draw a diagram to visualize the coffee table:
_______________________
/ /|
/ / |
/ / |
/______________________/ |
|______________________| /
| | /
| |/
/ height
/
/
width
Now, let's calculate the length of the diagonals.
The diagonal length is the hypotenuse of a right triangle formed by one of the dimensions (length, width, or height) as the base, and the other two dimensions as the legs.
For the length, the two legs of the right triangle are the width (24 inches) and the height (14 inches).
Using the Pythagorean theorem, the formula is:
diagonal length = √(width² + height²)
Substituting the values:
diagonal length = √(24² + 14²)
= √(576 + 196)
= √(772)
≈ 27.8 inches (rounded to the nearest tenth)
Therefore, Keisha should make each diagonal approximately 27.8 inches long.