Question

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

Answer 1

The length of a side of the square is 8 unit.

Explanation:

Suppose, the length of a side of the square is
`a` unit.

Formula for perimeter of square:
`P=4(side) = 4a`

Formula for area of square:
`A=(side)^2 = a^2`

Given that, the area is 32 more than the perimeter. So, the equation will be......

`a^2= 4a+32`

Moving all terms to the left side, we will get.....

`a^2-4a-32=0`

Now, factoring out the left side.......

`a^2-8a+4a-32=0\\ \\ a(a-8)+4(a-8)=0\\ \\ (a-8)(a+4)=0`

Using 'zero-product property', we will get......

`a-8=0\\ a=8\\ \\ and\\ \\ a+4=0\\ a=-4`

(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.