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 answer

To find the length of the diagonal of a rectangular prism, we can use the formula for the space diagonal, which is given by:

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

where:

  • \(l\) is the length,
  • \(w\) is the width,
  • \(h\) is the height.

For Keysha's coffee table, we have:

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

First, we will calculate \(l^2\), \(w^2\), and \(h^2\):

\[ l^2 = 44^2 = 1936 \]

\[ w^2 = 24^2 = 576 \]

\[ h^2 = 14^2 = 196 \]

Next, we can sum these values:

\[ l^2 + w^2 + h^2 = 1936 + 576 + 196 = 2708 \]

Now, we will take the square root to find the length of the diagonal:

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

Rounding to the nearest tenth, the length Keysha should make each diagonal is:

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