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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 Measures 82 Ft Find The Perimeter Of The Parking Lot class=

Sagot :

Corsaquix

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]

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