SOLUTION: the area of a square is numerically 117 more than the perimeter. Find the length of the side.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: the area of a square is numerically 117 more than the perimeter. Find the length of the side.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 660443: the area of a square is numerically 117 more than the perimeter. Find the length of the side.
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let s be the length of a side of the square. Then the perimeter of the square is 4%2As and the area is s%5E2
s%5E2+=+4s+%2B+117
s%5E2+-+4s+-+117+=+0
Factoring this equation gives
%28s+-+13%29%28s+%2B+9%29+=+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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ to solve for s, with a=1, b=-4 and c=-117.