Determine the side of a square if the area of the square is 45 more than the perimeter.

Expert Answers

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We cannot compare the perimeter and the area as they have different dimensions. So we use only the magnitudes here.

Let the side of the square be A.

SO the perimeter is 4*A.

The area is A^2.

As the magnitude of the area is 45 more than that of the perimeter.

A^2  = 4A + 45

=> A^2 - 4A - 45 = 0

=> A^2 + 5A - 9A - 45 = 0

=> A ( A + 5) -9( A + 5) = 0

=> (A + 5)(A -9) = 0

A is either -5 or 9.

But as A is the side of the square it cannot be negative. So we consider only 9

The side of the square is 9.

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