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
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.
I've already considered diffrentiating, but it doesn't produce an interger, so something in my calculations is probably off. I just need to know what.