Posted by mark on Thursday, March 21, 2013 at 3:10am.
if the squares have side x and y,
4x+4y=24
y = 6-x
area = x^2+y^2 = x^2 + (6-x)^2 = 2x^2 - 12x + 36
Now, that's a parabola which opens upward, so it has no maximum value. Since 0<=x<=6, the maximum area is reached at the endpoints of the interval.
So, maximum area is when there is just one large square, area 36.
If you must have two nonzero pieces of wire, then choose one to be very tiny and the other to be almost 24 cm.
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