In a triangle $A B C$ , if $r_{1} : r_{2}$ : $r_{3} = 2 : 4 : 6$ then $a : b : c =$

3 : 5 : 7

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1 : 2 : 3

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5 : 8 : 9

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3 : 4 : 5

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Solution

The correct option is C $5 : 8 : 9$
we know that $r_{1} = \frac{△}{(s - a)}$ and others similar

$\frac{△}{s - a}$ : $\frac{△}{s - b}$ : $\frac{△}{s - c}$ = $2 : 4 : 6$

$\frac{1}{s - a}$ : $\frac{1}{s - b}$ : $\frac{1}{s - c}$ = $2 : 4 : 6$

consider,
$\frac{1}{s - a} = 2 k$ , $\frac{1}{s - b} = 4 k$ , $\frac{1}{s - c} = 6 k$

then $s - a = \frac{1}{2 k}$ , $s - b = \frac{1}{4 k}$ , $s - c = \frac{1}{6 k}$

$a = \frac{5}{12 k}, b = \frac{8}{12 k}, c = \frac{9}{12 k}$

now after solving this we finds $a : b : c = 5 : 8 : 9$

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Similar questions

△ A B C, R, r, r_{1}, r_{2}, r_{3}

A, B, C

r_{1} : r_{2} : r_{3} = 1 : 2 : 3

r_{1} = 2, r_{2} = 3, r_{3} = 6

A B C

r_{1} = 2, r_{2} = 3

r_{3} = 6

a =

r_{1} = 2, r_{2} = 3

r_{3} = 6

a =

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