Question

There is a square parking lot at the grocery store. The diagonal of the parking lot measures 8√2 ft. Find the perimeter of the parking lot.​

Answer 1

Answer:

$32\:\mathrm{feet}$

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 $x:x:x\sqrt{2}$, where $x\sqrt{2}$ is the hypotenuse of the triangle and $x$ represents each of the two other sides of the triangle (from the Pythagorean Theorem).

Thus, we know that $8\sqrt{2}$ represents the hypotenuse, which means that the side length must be $8$ feet. The perimeter is then $4\cdot 8=\boxed{32\:\mathrm{feet}}$