In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y . if x²-c²=y, where c is the length of the third side of the triangle, then the circumradius of the triangle is

Step-by-step solution

Let two sides of triangle are a and b . aligned & a+b=x & a b=y & x²-c²=y (a+b)²-c²=a b &(a+b-c)(a+b+c)=a b & 2(s-c)(2 s)=a b & 4 s(s-c)=a b & s(s-c) a b = 1 4 & ² c 2 = 1 4 & c=- 1 2 c=120^ aligned Area of triangle is, = 1 2 a b ( 120^ )= 3 4 a b R= a b c 4 R = a b c 3 a b = c 3