Question

find the area of the largest rectangle having one side on the x axis and inscribed in the triangle formed by the lines y=x, y=0, and 3x + y = 20

Answer 1

if the height of the rectangle is y, the base of the rectangle is (20-y)/3 - y.

So, the area is y((20-y)/3 - y) = 4/3 (5y-y^2)

max area where 5-2y = 0, or y = 5/2.

So, the largest rectangle has area 50/3