Question 282707: The area of a square is 12 more than its perimeter. Find the length of a side. Found 2 solutions by mananth, ikleyn:Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website!
let side be x
Area of square =Side * Side = x^2
Perimeter of square = 4*side= 4x
Area is 12 times the perimeter
x^2 = 12 *4*x
x^2/x= 48
x=48
the side is 48
You can put this solution on YOUR website! .
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The area of a square is 12 more than its perimeter. Find the length of a side.
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The solution in the post by @mananth is incorrect, since his setup equation is incorrect.
I came to bring a correct solution.
Let x be the side length of the square.
The setup equation is
x^2 = 4x + 12,
according to the problem.
Reduce it to the standard form of a quadratic equation and factorize
x^2 - 4x - 12 = 0,
(x-6)*(x+2) = 0.
The roots are x= 6 and x= -2.
Since we look for a side length, we choose the positive root and reject the negative one.
ANSWER. The side of the square is 6 units.
Solved correctly.
You may check mentally that the answer value satisfies the problem's condition.
