Question

Question
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.

Answer 1

To find the length of the diagonal in a rectangular prism (coffee table), we can use the 3-dimensional version of the Pythagorean theorem. The diagonal \( d \) can be calculated using the formula:

\[
d = \sqrt{l^2 + w^2 + h^2}
\]

where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

Given:
- Length \( l = 44 \) inches,
- Width \( w = 24 \) inches,
- Height \( h = 14 \) inches.

Now we can substitute the values into the formula:

\[
d = \sqrt{44^2 + 24^2 + 14^2}
\]

Calculating each term:

\[
44^2 = 1936
\]
\[
24^2 = 576
\]
\[
14^2 = 196
\]

Now add these values together:

\[
1936 + 576 + 196 = 2708
\]

Next, we take the square root:

\[
d = \sqrt{2708}
\]

Calculating the square root:

\[
d \approx 52.0 \text{ (rounded to the nearest tenth)}
\]

Thus, the length Keysha should make each diagonal is approximately **52.0 inches**.