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)

1 answer

To find the length of the diagonals of a rectangular prism (in this case, the coffee table), we can use the three-dimensional diagonal formula. The formula for the length of the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by:

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

Given:

  • Length \( l = 44 \) in.
  • Width \( w = 24 \) in.
  • Height \( h = 14 \) in.

Now we 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:

\[ d = \sqrt{1936 + 576 + 196} \] \[ d = \sqrt{2708} \]

Now calculate \( \sqrt{2708} \):

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

Thus, the length of each diagonal, rounded to the nearest tenth, is:

\[ \boxed{52.0} \text{ in.} \]