Question

If bc:ac:ab=1:2:3,then find a/bc:b/ca

Answer 1

Given $bc:ac:ab=1:2:3$. So we can write

$bc=x\\ ac=2x\\ ab=3x\\ ax=2bx=3cx=y (say)\\ a=\frac{y}{x} ,b=\frac{y}{2x} ,c=\frac{y}{3x}$

Whrere $x$ is a real number.

Now,

$\frac{a}{bc} :\frac{b}{ca} =\frac{a(abc)}{bc} :\frac{b(abc)}{ca} \\ \frac{a}{bc} :\frac{b}{ca} =a^2:b^2\\ \frac{a}{bc} :\frac{b}{ca} =(\frac{y}{x} )^2: (\frac{y}{2x} )^2\\ \frac{a}{bc} :\frac{b}{ca} =1: \frac{1}{4}\\ \frac{a}{bc} :\frac{b}{ca} =4:1$