An open box has a rectangular base and its height is equal to the length of the shortest side of the base. What dimensions give a volume of 250 cubic centimeters using 200 square centimeters of material?
the area gives you
x^2 + 2(x+y)*x = 3x^2 + 2xy = 200
or,
y = (200-3x^2)/(2x)
Now, the volume gives
x^2 (200-3x^2)/(2x) = 250
The only solution I get is
x = 2.845
y = 30.873
I'll let you check to see that this fits the original problem.