a square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between the?
the difference between their areas is 24 suare feet, find the lengths of the sides of the poster and the sign.
Best answer:
Answer by Brian
Let x denote the area of the poster. Then, since the sign has sides that measure 2 feet less, the sides of the sign are x - 2.
Then, since the area of a square is s^2, we see that the area of the poster is x^2 and the area of the sign is (x - 2)^2. Since the difference between their areas is 24 ft^2, we have:
x^2 - (x - 2)^2 = 24
==> x^2 - (x^2 - 4x + 4) = 24, by expanding
==> 4x - 4 = 24
==> 4x = 28
==> x = 7.
Therefore, the poster's sides are 7 feet long and the sign has sides that are 5 feet long.
I hope this helps!
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