A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 52 square feet, find the lengths of the sides of the poster and the sign.

Let \(s=\) the length of a side of the sign
We get \(s-2=\) the length of a side of the poster

Difference between areas is 52
So \(s^{2}-(s-2)^{2}=52\)
⇒\(s^{2}-(s^{2}-4s+4)=52\)
⇒\(4s-4=52\)
⇒\(4s=56\)
⇒\(s=14\) is the length of a side of the sign

Plug into \(s-2=14-2=12\) is the length of a side of the poster

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A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 52 square​ feet, find the lengths of the sides of the poster and the sign.

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A square poster has sides measuring 2 feet less than the sides of a square sign. If the difference between their areas is 52 square feet, find the lengths of the sides of the poster and the sign.