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

We'll note as x the side of the
square.

We'll write the formula for the area of the
square:

A = x^2

We'll write
the formula for the perimeter of the square:

P =
4x

Now, we'll write mathematically the condition imposed by
enunciation:

x^2 - 60 = 4x (area is 60 less than the
perimeter)

We'll subtract both sides
4x:

x^2 - 4x - 60 = 4x -
4x

We'll eliminate like
terms:

x^2 - 4x - 60 = 0

We'll
apply the quadratic formula:

x1 = [4+sqrt(16 +
240)]/2

x1 = (4+16)/2

x1 =
10

x2 = (4-16)/2

x2 =
-6

Since the length of the side of the square cannot be
negative, we'll reject the second root x2 =
-6.

The length of the side of the square is x
= 10.