optimize area with a given length

I cannot seem to think or find a theoretical solution to this problem that is described in detail in the link given below. Is there a way of getting an approximate solution by numerically minimizing the objective area? I am not sure how to impose convexity so that I can minimize the objective area. Or even have a more rough idea by forcing the rope to gradually have 2, 3, 4, 5... corners and see what shapes do I get. Any hints help are highly appreciated. Thanks!

https://math.stackexchange.com/questions/2646832/how-to-place-a-rope-with-a-given-length-within-an-orthogonal-triangle-see-pictu