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A square poster has sides measuring 2 feet less than the sides of a square sign. Of the difference between their areas is 36 square feet, find the lengths of the sides of the poster and sign

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Answer: The length of the side of the square poster is 8 feet

The length of the side of the square sign is 10 feet

Explanation:

Let the length of one side of the square poster be x

Let the length of one side of the square sign be y

Since they are both squares, the area of a square is expressed as length^2

A square poster has sides measuring 2 feet less than the sides of a square sign. It means that

y = 2+x

If the difference between their areas is 36 square feet, it means that

y^2 - x^2 = 36 - - - - - - - 1

Substituting y = 2 + x into equation 1, it becomes

(2+x)^2 - x^2 = 36

4 + 4x + x^2 - x^2 = 36

4x = 36 - 4 = 32

x = 32/4 = 8

y = 2 + x = 2 + 8

y = 10

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