## Length of Side of Square

If the numerical value of the area of a square plus two times the numerical value of its perimeter is equal to $20$, what is the length of one side of the square?
Source: NCTM Mathematics Teacher, September 2006

Solution
Let $a$ represent the length of one side of a square. The following equation is true
$a^2+2(4a)=20$
$a^2+8a-20=0$
$(a-2)(a+10)=0$
$a=2$ or $a=-10$ (extraneous solution)
The length of one side of the square equals $2$ units.

Answer: $2$ units