Derivative (max/min) question (1 Viewer)

[QZP]

I'm stuck on this question: "A parallelogram is inscribed in a triangle so that they have one vertex in common. The other vertices of the parallelogram lie on the three different sides of the triangle. Show that the maximum area of the parallelogram is half that of the triangle."

I can't see a way to connect the dimensions/area the parallelogram with that of the triangle. :S
Hints please ^^

 

[QZP]

Bump

 

[braintic]

Solution attached:

View attachment Max Min question.pdf

 

[QZP]

Solution attached:

View attachment 29930

Very nice I was playing around with similar triangles but I got no where near completing the solution. Thanks!