The area of a square is 45 more square inches than its perimeter. What is the length of each side of the square?

Let x be one 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 = 4x + 45 (area is equal to the perimeter plus
45)

We'll subtract both sides 4x +
45:

x^2 - 4x - 45 = 4x + 45 - 4x -
45

We'll eliminate like terms:

x^2 - 4x
- 45 = 0

We'll pply the quadratic
formula:

x1 = [4+sqrt(16 + 180)]/2

x1 =
(4+14)/2

x1 = 9

x2 =
(4-14)/2

x2 = -5

Since the length of
the side of the square cannot be negative, we'll reject the second root x2 =
-5.

The length of the side of the square is x =
9.