SOLUTION: one side of a rectangle is 3cm longer than the other. The area of the rectangle is twice its perimeter .Find the dimensions of the rectangle Thank you

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Question 1200723: one side of a rectangle is 3cm longer than the other. The area of the rectangle is twice its perimeter .Find the dimensions of the rectangle Thank you
Answer by ikleyn(52781) About Me  (Show Source):
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one side of a rectangle is 3cm longer than the other.
The area of the rectangle is twice its perimeter .
Find the dimensions of the rectangle Thank you
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x = one side
x+3 = the other side.


The area = x*(x+3)

The perimeter = 2(x + (x+3)) = 2(2x+3) = 4x + 6


Equation

    x*(x+3) = 2(4x + 6)

    x^2 + 3x - 8x - 12 = 0

    x^2 - 5x - 12 = 0

    x%5B1%2C2%5D = %285+%2B-+sqrt%285%5E2+%2B+4%2A12%29%29%2F2 = %285+%2B-+sqrt%2873%29%29%2F2.


    The unique solution to the problem is the positive root x = %285+%2B+sqrt%2873%29%29%2F2 = 6.772001873.


The dimensions are 6.772001873 cm  and  9.772001873 cm.


CHECK.  The area is  6.772001873*9.772001873 = 66.17601499 cm^2;  

        the perimeter is  2*(6.772001873+9.772001873) = 33.08800749 cm.

        the ratio of these numbers is  66.17601499%2F33.08800749 = 2.000000000302  close enough to 2.

Solved.