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this part: ( the top quarter of the wire is 4x the bottom 3/4 is 10-4x) doesn't make any sense to me. as for hte rest of it, well, it's a related rates problem, isn't it?
so, what's the area of a circle? A = πr^2
what about the circumfrence? C = 2*π*r
what's the area of an equilateral triangle? A = 1/2*x*h, where h = the height of the triangle
sin60(degrees) = h/x, so h = xsin60,
so A = 1/2*x*xsin60.
now the trick is to relate all of those, so that you eliminate all the variables besides x.
first step: A = π*r^2 + 1/2*x*x*sin60. only radius isn't meaningful right now, so get rid of using the circumference equation. that's how I'd approach it, anyway. remember that the circumference of your circle will be 10 - 3x, where x is the length of a side of your triangle!
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