Bot GPT 4-o mini 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.
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