Find the area of the largest rectangle that fits into the triangle with sides x = 0, y = 0, and x/4 + y/6 = 1.

Answer 1

The corner of the rectangle will have co-ordinates (x,6-(3/2)x)

The area will be A = (1/4)(24x-6x²)

The derivative is 6-3x and will be zero when x = 2

You figure the area!