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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Area and perimeter have different units, so I'll consider only their numeric values. Let the side of the square be S.

The perimeter is 4S and the area is S^2

As the area is 60 more than the perimeter

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

S = -6 and S = 10

As length is positive we eliminate S = -6

The side of the square is 10

Approved by eNotes Editorial Team