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 a rectangular prism, we can use the 3D distance formula, which is given by:

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

where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the rectangular prism.

In this case, the measurements are:

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

Plugging in these 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:

\[ 1936 + 576 + 196 = 2708 \]

Next, we take the square root:

\[ d = \sqrt{2708} \approx 52.0 \text{ in. (after rounding to the nearest tenth)} \]

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