Question

in an equilateral triangle the circumradius is n times then n is equal to

Answer 1

we know from properties of triangle.

circumradius of any triangle of side length a , b and c is given by

R = abc/4A

where A is area of that triangle.

Inradius of the triangle is given by r = A/S where S is semi perimeter of that triangle.

in case of equilateral triangle ,  

a = b = c = k

Then, R = k^3/4√3/4 k^2 = k/2√3

Ratio of R and r = k/√3/k/2√3 = 2:1

If there is any confusion please leave a comment below.