# Maximizing the area of rectangle inscribed in triangle

I'd like to ask if someone could help me out with this problem.

Let's have a triangle with coordinates $[0,0],[4,0],[1,3]$. Inscribe a rectangle into this triangle, so its area is maximized The base of rectangle lays on axis $x$.

I know how to proceed if it's a right triangle, but don't know how to proceed now.

• If it is not a right-angled triangle, you will find an optimal rectange has one side on an edge of the triangle, centred at the midpoint of that edge. Solve the question for one edge, and the solution on the other edges will be obvious. – Henry Jan 13 '14 at 10:40
• – StubbornAtom Feb 3 '17 at 14:31