The area of a square is 32 more than its perimeter. find the length of a side.

Answer:The length of a side of the square is 8 unit.Step-by-step explanation:Suppose, the length of a side of the square is [tex]a[/tex] unit. Formula for perimeter of square:  [tex]P=4(side) = 4a[/tex]Formula for area of square:   [tex]A=(side)^2 = a^2[/tex]Given that, the area is 32 more than the perimeter. So, the equation will be......[tex]a^2= 4a+32[/tex]Moving all terms to the left side, we will get.....[tex]a^2-4a-32=0[/tex]Now, factoring out the left side.......[tex]a^2-8a+4a-32=0\\ \\ a(a-8)+4(a-8)=0\\ \\ (a-8)(a+4)=0[/tex]Using 'zero-product property', we will get......[tex]a-8=0\\ a=8\\ \\ and\\ \\ a+4=0\\ a=-4[/tex] (Negative value is ignored as the side length can't be in negative)So, the length of a side of the square is 8 unit.