How to figure out this calculus optimization problem?

You may follow the following steps.
If you draw the figure, you will find, the main rectangle is divided into two equivalent triangles which are also in turn equivalent to the main triangle.(Hope the figure is readable. Base is 4 and vertical is 3)
     o
     |...o
     |--------o
     |.y.....|.... o
     |____ |______o
         x      
Take the side of the rectangle adjacent to the base as x and the other side as y. So the area is              A=xy...............(1)

Now, the equivalent triangle produces (4-x)/y=4/3
thus,                                                y=(12-3x)/4=3-3x/4....................(2)
So replacing 2 in 1,
A=x(2-2x/4)=3x-3(x^2)/4
Taking derivatiive w.r.t. x
dA/dx=3-3x/2
As dA/dx=0 for maxima,
x=2 and so from 2, y=3/2