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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.​

There is a square parking lot at the grocery store. The diagonal of the parking lot-example-1
User Darcelle
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1 Answer

4 votes

Answer:


32\:\mathrm{feet}

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√(2), where
x√(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√(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}}

User Naaz Muhammadh
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