Question

∆ABC ~ ∆LMN. In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ABC and ∆LMN such that $\frac{\mathrm{BC}}{\mathrm{MN}}=\frac{5}{4}.$

Answer 1

Construct ∆ABC such that AB = 5.5 cm, BC = 6 cm and CA = 4.5 cm.

∆ABC and ∆LMN are similar.

Therefore, their corresponding sides are proportional.

$\therefore \frac{\mathrm{AB}}{\mathrm{LM}}=\frac{\mathrm{BC}}{\mathrm{MN}}=\frac{\mathrm{CA}}{\mathrm{NL}}=\frac{5}{4}$

$\Rightarrow \frac{5.5}{\mathrm{LM}}=\frac{6}{\mathrm{MN}}=\frac{4.5}{\mathrm{NL}}=\frac{5}{4}$

$\Rightarrow \mathrm{LM}=\frac{4}{5}\times 5.5=4.4\mathrm{cm},\mathrm{MN}=\frac{4}{5}\times 6=4.8\mathrm{cm},\mathrm{NL}=\frac{4}{5}\times 4.5=3.6\mathrm{cm}$

Now, construct ∆LMN such that LM = 4.4 cm, MN = 4.8 cm and NL = 3.6 cm.