"a string 10 m long is cut in 2 so that one piece forms one square and one piece forms an equlateral triangle". HOw do you cut it so the total area obtained is minimalized...and part b. maximalized?

For maximalized i got that everything must go into the square, which makes sense...because at a given perimeter the area is bigger in a polygon with a larger number of sides, of course. But the minimum comes out to be at about 4.45 (if i remember right) meters into the square. Now...why isn't everything going into the triangle? I got some equations but I don't know how to write them in the 'cool way' so i won't even bother.