Answer: In a 45-45-90 triangle, the sides are in the ratio \(1:1:\sqrt{2}\). For a square, the diagonal cuts the square into two congruent 45-45-90 triangles.
Let \(s\) be the side length of the square (which is 4 feet in this case).
The diagonal length (\(d\)) is related to the side length (\(s\)) by the ratio \(1:\sqrt{2}\). Therefore,
\[ d = s \cdot \sqrt{2} \]
Substitute the given side length (\(s = 4\) feet) into the formula:
\[ d = 4 \cdot \sqrt{2} \]
Now, calculate the value:
\[ d = 4 \cdot 1.414 \approx 5.656 \]
So, the diagonal length of the projector screen is approximately 5.656 feet.
