A rectangle with sides of lengths a and b (a>b) is cut into rightangled triangles so that any two of these triangles either have a common side, a common vertex or no common points. Moreover, any common side of two triangles is a leg of one of them and the hypotenuse of the other. Prove that a>2b.(A Shapovalov) geometryrectanglegeometric inequalitycombinatoricscombinatorial geometry