Prove that a triangle with rational sides and rational area can be formed by pasting together two right triangles with the same property.

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewestHint: If the area and the sides are rational, then the height is also going to be rational. Drop a perpendicular from A to BC, meeting the side at D. Now you only need to prove that the side is divided into two rational parts – Vishnu C · 2 years ago

Log in to reply

(A+B)/( X+Y) = (A-B)(A+B)/C Or A-B , A+B, C are rational witch means (A-B)*(A+B)/C = X-Y is rational. C = X+ Y is rational => C + X - Y is also rational : C+ X-Y = 2X, 2X rational => X rational : X is rational and C is rational : C - X = Y is also rational. Hence X & Y are both rational. You did the same ? – Mohamed Laghlal · 2 years agoLog in to reply

– Raghav Vaidyanathan · 2 years ago

Nice use of contradiction. +1Log in to reply