Question

A pentagon has a perimeter of 20ft. If every side is halved, find the new perimeter

Answer 1

Answer: 10 feet

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How to get this answer:

A pentagon has 5 sides. If each side is the same length, then each side is 20/5 = 4 feet long. That halves to 4/2 = 2 feet. Each side is now 2 feet long, and there are 5 total sides, so 2*5 = 10 feet is the new perimeter.

A shortcut is to simply divide the perimeter in half to get 20/2 = 10. The reason why this works is because the perimeter is the sum of all the sides, which are all being cut in half.

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Algebraically, if we had the five sides a,b,c,d,e then

P = a+b+c+d+e

is the perimeter

Cutting each side in half gives

0.5*a+0.5*b+0.5*c+0.5*d+0.5*e = 0.5*(a+b+c+d+e) = 0.5*P

showing that we've cut the perimeter in half.