A square Turkish rug is sold at auction. The area of the Turkish rug in square feet is 12 more than its perimeter in feet. Find the length in feet of the side.

1. Problem Description

A square Turkish rug is sold at auction. The area of the Turkish rug in square feet is 12 more than its perimeter in feet. Find the length in feet of the side.

2. Solution Steps

Let $s$ be the length of the side of the square rug in feet.

The area of the square is $A = s^2$.

The perimeter of the square is $P = 4s$.

The problem states that the area is 12 more than the perimeter.

Therefore, we have the equation $A = P + 12$.

Substituting the formulas for area and perimeter, we get

$s^2 = 4s + 12$.

To solve for $s$, we rearrange the equation into a quadratic equation:

$s^2 - 4s - 12 = 0$.

We can factor this quadratic equation:

$(s - 6)(s + 2) = 0$.

The solutions are $s = 6$ and $s = -2$.

Since the side length of a rug cannot be negative, we have $s = 6$.

3. Final Answer

6