Answer:
[tex]32\:\mathrm{feet}[/tex]
Step-by-step explanation:
The square forms two 45-45-90 triangles, where the diagonal of the square is the hypotenuse of both these triangles. In all 45-45-90 triangles, the sides are in the ratio [tex]x:x:x\sqrt{2}[/tex], where [tex]x\sqrt{2}[/tex] is the hypotenuse of the triangle and [tex]x[/tex] represents each of the two other sides of the triangle (from the Pythagorean Theorem).
Thus, we know that [tex]8\sqrt{2}[/tex] represents the hypotenuse, which means that the side length must be [tex]8[/tex] feet. The perimeter is then [tex]4\cdot 8=\boxed{32\:\mathrm{feet}}[/tex]
