The area of a square is 117 more than the perimeter. Find length of the side.?

Answer 1

OK

If the square has side x, then
perimeter = 4x
Area = x²

The area of a square is 117 more than the perimeter then means
x² = 4x + 117

We need to solve the quadratic equation

x² - 4x - 117 = 0

You can now factorize x² - 4x - 117, or you can use the quadratic formula:

x = (4 ± √[4² + 4·117])/2 = (4 ± 22)/2
x = 13 or x = -9

A side of a square can not have negative length, therefore
the length of a side is 13 units.

Hope this helps.

Answer 2

Side = 13
Set up: Area = perimeter + 117
s^2 = 4s + 117 (move things around)
s^2 -4s -117 = 0 (Factor)
(s+9)(s-13) = 0 (which means)
s + 9 = 0 or s - 13 = 0 (which means)
s = -9 or x = 13 Sides can't be negative, so each side is 13

Answer 3

n^2 = 4n + 117 where n is the length of one side.
n^2 - 4n - 117 = 0
(n -13)(n+9) = 0
n = 13 units = one side of the square.

(Can't be the negative number for the other factor.)