Hi, I have been staring at this problem for ages now. I have a feeling I am being completely stupid but I cannot solve it. Help would be much appreciated!

This is one of the 'harder questions' in the topic of differentiation 2 in Maths AS-Level.

An equilateral triangle of side length 4cm has a rectangle inscribed in it as shown below:

(I hopefully attached a diagram I drew)

Show that the area of this rectangle is 2√3 (2x - x²)

The question goes on to ask to b) find the maximum possible area of the rectangle, and c) what proportion of the triangle is the rectangle in this case? I can handle part b) but I have no idea how to do c) either.

Thank you!

Post-Edit: I just realised i think this is in the wrong forum... I am not sure where to put it though.