Question

A triangle has sides with lengths of 2, 9, and 8. What is the radius of the triangles inscribed circle?

Answer 1

Radius of the inscribed circle `r=0.77(2dp)` unit.

Explanation:

sides of the triangle are `a=2 ; b=9; c=8`. Semi perimeter of the triangle `s=(2+9+8)/2=9.5 ; s-a= 7.5; s-b= 0.5 ; s-c= 1.5 :. A_t=sqrt(9.5*7.5*0.5*1.5)=7.31 sq.unit`. Where `A_t` is the area of triangle`=sqrt (s*(s-a)(s-b)(s-c))`. Radius of the inscribed circle `r=A_t/s= 7.31/9.5=0.77(2dp)`unit [Ans]