Mathematics - Properties of Triangle Question with Solution | TestHub

Let a=4k,b=5k,c=6k and s=15k/2. Heron's formula gives ${\Delta }^2$=s(s-a)(s-b)(s-c)=(15·7·5·3/16)k⁴=1575k⁴/16. Using R=abc/(4$\Delta$) and r=$\Delta$/s, R/r=abc·s/(4${\Delta }^2$)=($120k^3$)(15k/2)/(1575k⁴/4)=16/7.