Find the length of the side of a square if it's area is 60 more than its perimeter.

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Let the length of the side of the square be S.

Now the perimeter is given by 4S and the area if given by S^2.

We cannot say that area is 60 more than the perimeter as they have different units. We can say the same only about their magnitude.

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Let the length of the side of the square be S.

Now the perimeter is given by 4S and the area if given by S^2.

We cannot say that area is 60 more than the perimeter as they have different units. We can say the same only about their magnitude.

Doing that S^2 = 4S + 60

=> S^2 - 4S - 60 = 0

=> S^2 - 10S + 6S - 60 = 0

=> S(S - 10) + 6( S - 10) = 0

=> (S + 6)(S - 10) = 0

So we have S = -6 or 10.

Now length cannot be negative, so we ignore S = -6.

The length of the side of the square is 10.

Approved by eNotes Editorial Team