If a : b = 2 : 3 and b : c = 4 : 5, find a² : b² : bc = ?

14 : 9 : 45
216 : 36 : 45
316 : 36 : 20
44 : 36 : 40

Answer:- 1

Explanation:-

Solution:

\begin{aligned} a : b = 2 : 3 and b : c = 4 : 5 \\ a b c \\ 2_{\times (4)} 3_{\times (4)} \\ 4_{\times (3)} 5_{\times (3)} \\ \bar{\underline{8 12 15}} \\ ∴ a^{2} : b^{2} : b c \\ \Rightarrow {(8)}^{2} : {(12)}^{2} : (12 \times 15) \\ \Rightarrow 64 : 144 : 180 \end{aligned}

$\eqalign{ & a:b = 2:3{\text{ and }}b:c = 4:5 \cr & a{\text{ }}\,\,\,\,\,\,\,\,\,\,\,{\text{ }}b{\text{ }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ }}c \cr & {2_{ \times \left( 4 \right)}}\,\,\,\,{\text{ }}{3_{ \times \left( 4 \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{4_{ \times \left( 3 \right)}}\,\,\,\,\,\,\,\,{\text{ }}{5_{ \times \left( 3 \right)}} \cr & \overline {\underline {\,\,8{\text{ }}\,\,\,\,\,\,\,\,\,\,{\text{ }}12{\text{ }}\,\,\,\,\,\,\,\,\,\,\,{\text{ }}15{\text{ }}\,\,{\text{ }}} } \cr & \therefore {a^2}:{b^2}:bc \cr & \Rightarrow {\left( 8 \right)^2}:{\left( {12} \right)^2}:\left( {12 \times 15} \right) \cr & \Rightarrow 64:144:180 \cr}$