Question

If $a:b=2:3$ and $b:c=4:5$, find $a^2:b^2:bc$.

• A. $4:9:45$
• B. $16:36:45$
• C. $16:36:20$
• D. $4:36:20$

Answer 1

Answer: (B)

$16:36:45$

$a:b=2:3\Rightarrow \frac{a}{b}=\frac{2}{3}\Rightarrow a=\frac{2b}{3}\Rightarrow a^2=\frac{4b^2}{9}$

$b:c=4:5\Rightarrow \frac{b}{c}=\frac{4}{5}\Rightarrow b=\frac{4c}{5}\Rightarrow b^2=\frac{4bc}{5}\Rightarrow bc=\frac{5b^2}{4}$

$\therefore a^2:b^2:bc=\frac{4b^2}{9}:b^2:\frac{5b^2}{4}=\frac{4}{9}:1:\frac{5}{4}$

$=\frac{4}{9}\times 36:1\times 36:\frac{5}{4}\times 36$ $(\because LCM=36)$

$=16:36:45.$