Question

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

Answer 1

$\textbf{Given:}$

$bc:ac:ab=1:2:3$

$\textbf{To find:}$

$\frac{a}{bc}:\frac{b}{ca}$

$\textbf{Solution:}$

$bc:ac:ab=1:2:3$

$\text{Then,}$

$bc=k,\;ac=2k,\;ab=3k$

$\text{Multiplying the above 3 equations, we get}$

$a^2b^2c^2=6\,k^3$..........(1)

$\text{Now,}$

$\dfrac{a}{bc}:\dfrac{b}{ca}$

$\text{Multiply by abc}$

$=\dfrac{a(abc)}{bc}:\dfrac{b(abc)}{ca}$

$=a^2:b^2$

$=\dfrac{6k^3}{b^2c^2}:\dfrac{6k^3}{a^2c^2}$ $\text{(Using (1))}$

$=\dfrac{6k^3}{(bc)^2}:\dfrac{6k^3}{(ac)^2}$

$=\dfrac{6k^3}{k^2}:\dfrac{6k^3}{4k^2}$

$=6k:\dfrac{6k}{4}$

$=1:\dfrac{1}{4}$

$=4:1$

$\therefore\bf\dfrac{a}{bc}:\dfrac{b}{ca}=4:1$

Find more:

If a ratio B equal to 3 ratio 5 and b ratio c equal to 6 ratios 7 find a ratio B ratio c

https://brainly.in/question/5994105

If X:Y:Z=4:3:2 and x^2+ y^2+ z^2 =11600, then

the value of √X+Y-Z is equals to

https://brainly.in/question/14136378