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iren [92.7K]
3 years ago
8

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 p

arking lot.​

Mathematics
1 answer:
valkas [14]3 years ago
3 0

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}}

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