Question

Triangles Unit Test
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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.(1 point)
in.

Answer 1

To find the length of the diagonal of the rectangular prism (the coffee table), you can use the 3D version of the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is:

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

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

Now, plug in the values:

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

Calculating each term:

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

Now, add these values together:

\[
1936 + 576 + 196 = 2708
\]

Now, take the square root of the sum:

\[
d = \sqrt{2708} \approx 52.0
\]

So, the length Keysha should make each diagonal is approximately **52.0 inches** when rounded to the nearest tenth.