SOLUTION: hi, I need some help with this: "The area of a certain square is one-half the area of the rectangle formed if the length of one side of the original square is increased by nine

Question 1120817: hi, I need some help with this:
"The area of a certain square is one-half the area of the rectangle formed if the length of one side of the original square is increased by nine and the adjacent side is increased by six. What is the perimeter of the square?"
Thank you!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let x be the length of a side of the square
:
x^2 = (x+9) * (x+6) / 2
:
2x^2 = x^2 +15x +54
:
x^2 -15x -54 = 0
:
(x-18) * (x+3) = 0
:
x = 18 and x = -3
:
we reject the negative value for side x
:
the length of a side of the square is 18
:
*******************************************
the perimeter of the square is 4 * 18 = 72
*******************************************
:
check the answer
:
18^2 = (18+9) * (18+6) / 2
:
324 = 648 / 2 = 324
:
the answer checks
:
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