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Let x represent the width of the rectangle. Then 2x represents the length of the rectangle. That means that the perimeter of the rectangle is 6x and the perimeter of the square is then
(36-6x=6-x) so the side of the square must measure (6-x)
The area of the rectangle is then (2x^2)and the area of the square is (6-x)^2=36-12x+x^2 and the sum of these two areas gives the total area function with respect to the width of the rectangle:
A(x) = 3x^2-12x + 36
for which you want to find a minimum value
By using quadratic formula, we have;
x= -(-12) / (2)(3)
x = 6 inch
This is the width of rectangle that shall minimize the area.
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