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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
= = .
The unique solution to the problem is the positive root x = = 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 = 2.000000000302 close enough to 2.
Solved.