Question

$\Delta ABC\sim \Delta LMN$. In $\Delta ABC$ AB=5.5cm, BC = 6cm and AC = 4.5cm.Construct $\Delta ABC$ and $\Delta LMN$ such that $\frac{LM}{AB}=\frac{5}{4}$. Then the measure of MN =_________ cm.

• A. 6.8 cm
• B. 7.5 cm
• C. 4.5 cm
• D. 5.8 cm

Answer 1

The correct option is B 7.5 cm

Given $\Delta ABC\sim \Delta LMN$, therefore corresponding sides will be in the same ratio.

ie, $\frac{LM}{AB}=\frac{MN}{BC}=\frac{NL}{CA}=\frac{5}{4}$

$\to \frac{MN}{BC}=\frac{5}{4}\frac{MN}{6}=\frac{5}{4}$

$\to MN=\frac{5}{4}\times 6=7.5cm$