To find the length of the diagonal in a rectangular prism (coffee table), we can use the 3-dimensional version of the Pythagorean theorem. The diagonal \( d \) can be calculated using the formula:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( l \) 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 we can 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 together:
\[ 1936 + 576 + 196 = 2708 \]
Next, we take the square root:
\[ d = \sqrt{2708} \]
Calculating the square root:
\[ d \approx 52.0 \text{ (rounded to the nearest tenth)} \]
Thus, the length Keysha should make each diagonal is approximately 52.0 inches.
1 answer