If in a triangle ABC $r_{1} = 2 r_{2} = 3 r_{3}$ , then the perimeter of the triangle is

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Solution

The correct option is C 3b
Given, $r_{1} = 2 r_{2} = 3 r_{3}$

$\Rightarrow \frac{Δ}{s - a} = \frac{2 Δ}{s - b} = \frac{3 Δ}{s - c}$

$\Rightarrow \frac{s - a}{s - b} = \frac{1}{2}, \frac{s - c}{s - b} = \frac{3}{2}$

$\Rightarrow \frac{s - a + s - c}{s - b} = 2$

$\Rightarrow 2 s - a - c = 2 s - 2 b$

$\Rightarrow a + b + c = 3 b$

$\Rightarrow 2 s = 3 b$

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