Question

∆ ABC ∆ RSM and if AB =10, BC=12,RS= 5 find SM​

Answer 1

Given : ∆ ABC ≈  ∆RSM

AB =10, BC=12,RS= 5

To Find : SM

Solution:

∆ ABC ≈  ∆RSM

corresponding sides of similar triangles are in same proportion

Hence

AB/RS  = BC/SM  = AC/RM

AB/RS = BC/ SM

=> 10/5  = 12 /SM

=> 2 = 12/SM

=> SM = 12/2

=> SM = 6

Length of SM = 6

Answer 2

Answer:

$\bf \green {Here}$

∆ABC∼∆RSM

$\bf \blue {Given}$

$\sf \purple \implies \pink {AB = 10 cm}$

$\sf \orange \implies \red {BC = 12 cm}$

$\sf \pink \implies \purple {RS = 5 cm}$

$\sf \red \implies \orange {SM = ?}$

We know,

$\begin{gathered} = \sf{\dfrac{AB}{RS} = \dfrac{BC}{SM}} \\ \\ \sf\implies SM = \dfrac{BC}{\dfrac{AB}{RS}} \\ \\ \sf\implies SM = \dfrac{12}{ \dfrac{10}{5} } \\ \\ \sf\implies SM = \dfrac{12 \times 5}{10} \\ \\ \sf\implies SM = \dfrac{60}{10} \\ \\ \sf\implies SM = \blue { 6 \: cm}\end{gathered}$