To find the length of the diagonal of the rectangular prism (coffee table), we can use the 3D diagonal formula:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( d \) is the length of the diagonal,
- \( l \) 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, substitute the values into the formula:
\[ d = \sqrt{(44)^2 + (24)^2 + (14)^2} \]
Calculating each component:
\[ (44)^2 = 1936 \]
\[ (24)^2 = 576 \]
\[ (14)^2 = 196 \]
Now, add these values together:
\[ d = \sqrt{1936 + 576 + 196} = \sqrt{2708} \]
Calculating the square root:
\[ d \approx 52.0 \text{ inches} \quad (\text{to the nearest tenth}) \]
Thus, the length Keysha should make each diagonal is 52.0 in.