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
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<pre>
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[1,2]}}} = {{{(5 +- sqrt(5^2 + 4*12))/2}}} = {{{(5 +- sqrt(73))/2}}}.


    The unique solution to the problem is the positive root x = {{{(5 + sqrt(73))/2}}} = 6.772001873.


The dimensions are 6.772001873 cm  and  9.772001873 cm.


<U>CHECK</U>.  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  {{{66.17601499/33.08800749}}} = 2.000000000302  close enough to 2.
</pre>

Solved.