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**DemonX01** A 30 cm piece of wire is cut into two. One piece is bent into the shape of a square, the other piece into the shape of a rectangle with a length-to-width ratio of 2:1. What are the lengths of the two pieces if the sum of the areas of the square and rectangle is a minimum?

This is what I did so far:

Let x represent the width of the rectangle

" y " square

" z " sum of the areas

30=2x+2x+x+x+4y

=6x+4y

7.5=y+1.5x

y=7.5-1.5x

z=y^2+2x^2

=(7.5-1.5x)^2+2x^2

=4.25x^2-22.5x+56.25

but then when I try finding the vertex, by completing the square, I don't get an integer. I'm not sure what to do.