# The area of a square is 45 more than the perimeter. How do you find the length of the side?

##### 1 Answer

Length of one side is 9 units.

Rather than doing a straight factorising approach I have used the formula to demonstrate its use.

#### Explanation:

As it is a square the length of all the sides is the same.

Let the length of 1 side be L

Let the area be A

Then

Perimeter is

The question states: "The area of a square is 45 more than.."

Substitute equation (3) into equation (1) giving:

So now we are able to write just 1 equation with 1 unknown, which is solvable.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtract

The conditions that satisfy this equation equalling zero gives us the potential size of L

Using

Of these two

So area does indeed equal sum of sides + 45