Question

The sides of a right angled triangle are 2x +1,2x-1, x +2 find their sides and area,

Answer 1

The only constraint for this problem as stated is that the triangle inequality must be satisfied; that is, the sum of the lengths of the shorter sides must be greater than the length of the longest. This requires that 2x+2x-1 be greater than 2x+1. This inequality is satisfied by any value of x greater than 1. If it is further required that the triangle be a right triangle then setting the sum of the squares of the shorter sides equal to the square of the longest gives x=2 as the only positive solution.