Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.

If $r_1=2r_2=3r_3,$ then $a:b$ is equal to?

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $\frac{7}{4}$
• D. $\frac{4}{7}$

Answer 1

The correct option is A $\frac{5}{4}$

$r_1=2r_2=3r_3$
$\Rightarrow \frac{△}{s-a}=\frac{2△}{s-b}=\frac{3△}{s-c}$
$\Rightarrow s-b=2(s-a)$
$\Rightarrow \frac{a+b+c}{2}-b=2(\frac{a+b+c}{2}-a)$
$\Rightarrow 3a-3b=c$ ...(1)
$\Rightarrow s-c=3(s-a)$
$\Rightarrow \frac{a+b+c}{2}-c=3(\frac{a+b+c}{2}-a)$
$\Rightarrow a-\frac{b}{2}=c$ ...(2)
From (1) and (2): $3a-3b=a-\frac{b}{2}$
$\Rightarrow \frac{a}{b}=\frac{5}{4}$
Ans: A