In triangle ABC,if r_1=36, r_2=18 and r_3=12, | vedclass

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(D) Given in a $	riangle ABC$: $r_1 = \frac{\Delta}{s-a} = 36, r_2 = \frac{\Delta}{s-b} = 18, r_3 = \frac{\Delta}{s-c} = 12$ $\frac{1}{r_1} + \frac{1

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$54$

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(D) Given in a $	riangle ABC$: $r_1 = \frac{\Delta}{s-a} = 36, r_2 = \frac{\Delta}{s-b} = 18, r_3 = \frac{\Delta}{s-c} = 12$ $\frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3} = \frac{1}{36} + \frac{1}{18} + \frac{1}{12} = \frac{1+2+3}{36} = \frac{6}{36} = \frac{1}{6}$ Since $\frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3} = \frac{s}{\Delta}$,we have $\frac{s}{\Delta} = \frac{1}{6} \Rightarrow \Delta = 6s$ $r_1 = \frac{6s}{s-a} = 36$ $\Rightarrow 6s = 36s - 36a$ $\Rightarrow 36a = 30s$ $\Rightarrow a = \frac{5s}{6}$ $r_2 = \frac{6s}{s-b} = 18$ $\Rightarrow 6s = 18s - 18b$ $\Rightarrow 18b = 12s$ $\Rightarrow b = \frac{2s}{3}$ $r_3 = \frac{6s}{s-c} = 12$ $\Rightarrow 6s = 12s - 12c$ $\Rightarrow 12c = 6s$ $\Rightarrow c = \frac{s}{2}$ Using Heron's formula $\Delta^2 = s(s-a)(s-b)(s-c) = (6s)^2 = 36s^2$ $s(s - \frac{5s}{6})(s - \frac{2s}{3})(s - \frac{s}{2}) = 36s^2$ $s(\frac{s}{6})(\frac{s}{3})(\frac{s}{2}) = 36s^2$ $\frac{s^4}{36} = 36s^2$ $\Rightarrow s^2 = 36^2$ $\Rightarrow s = 36$ $a = \frac{5 	imes 36}{6} = 30$ $b = \frac{2 	imes 36}{3} = 24$ $a+b = 30+24 = 54$

In triangle $ABC$,if $r_1=36, r_2=18$ and $r_3=12$,then $a+b=$

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