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 [tex]s=[/tex] the length of a side of the sign
We get [tex]s-2=[/tex] the length of a side of the poster

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

Plug into [tex]s-2=14-2=12[/tex] 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.