Find the Number

Geometry Level 3

The product of the perimeter of a triangle, the radius of its in-circle, and a number gives the area of the triangle. The number is

1 solution

Rohan Shinde
Dec 31, 2018

Let inradius be $r$ , semiperimeter be $s$ , and area of triangle be $\Delta$ .

It is quite well known that $r=\frac {\Delta}{s}$

Hence $\Delta=rs$

From given conditions, for a real number $k$ we have $2rsk=\Delta$

That means $2k\Delta=\Delta$

Implying $k=0.5$