Question

The area of a square is 12 more than its perimeter. find the length of a side and its perimeter.

Answer 1

The area of a square is 12 more than its perimeter.

Let the side of the square be x.

Then area of the square =$\\ \ x*x=x^2$

and the perimeter=4x

As per the problem

Area-Perimeter=12

$\\ \ x^2-4x=12\\ \\ \Rightarrow x^2-4x-12=0\\ \\ \Rightarrow x^2-6x+2x-12=0\\ \\ \Rightarrow x(x-6)+2(x-6)=0\\ \\ \Rightarrow (x-6)(x+2)=0\\ \\ \Rightarrow x=6,-2$

x can not be negative. Hence x=6.

side length=x=6

Perimeter=4x=24