Question 660443
Let s be the length of a side of the square.  Then the perimeter of the square is {{{4*s}}} and the area is {{{s^2}}}
{{{s^2 = 4s + 117}}}
{{{s^2 - 4s - 117 = 0}}}
Factoring this equation gives
{{{(s - 13)(s + 9) = 0}}}
So we have s = 13 or s = -9.  Since the side of a square cannot have negative length, the side must be 13.  The perimeter would be 52 and the area would be 169.
You could also use the quadratic equation {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} to solve for s, with a=1, b=-4 and c=-117.