If in a $ riangle A B C, r_1=2 r_2=3 r_3$, then the perimeter of the triangle is equal to

Question

If in a $	riangle A B C, r_1=2 r_2=3 r_3$, then the perimeter of the triangle is equal to

Aicharya · Accepted Answer

Given that, $r_1=2 r_2=3 r_3$

Now, adding Eqs. (i), (ii) and (iii), we get $\begin{aligned} & (s-a)+(s-b)+(s-c)=\Delta \mathrm{K}+2 \Delta \mathrm{K}+3 \Delta K \\ & 3 s-(a+b+c)=6 \Delta K \end{aligned}$ Since, we know $a+b+c=2 s$

$\begin{aligned} & 3 s-2 s=3(s-b) \\ & s=3 s-3 b \\ & 2 s=3 b\end{aligned}$

If in a $\triangle A B C, r_1=2 r_2=3 r_3$, then the perimeter of the triangle is equal to

Solution