A box with an open top is made from a square piece of cardboard, of which side length is 100 cm, by cutting a square from each corner and then folding up the sides. Find the dimensions of the box of the largest volume.

I drew a diagram and on any given side of 100 cm your going to have two pieces being cut away so I made the sum of the pieces and part left over

and so

and

solving

my interval is

Is this correct so far? because if x = 50 than 2x=100 which doesn't seem right to me