Question

If $\Delta ABC\sim \Delta DEF$ such that area of $\Delta ABC$ is $9c{m}^2$ and the area of $\Delta DEF$ is $16c{m}^2$ and BC = 2.1 cm, then the length of EF is

• A. 1.4 cm
• B. 3.6 cm
• C. 5.4 cm
• D. 2.8 cm

Answer 1

The correct option is D 2.8 cm

We have ,

$\Delta ABC\sim \Delta DEF$

$\Rightarrow \frac{area\left(\Delta ABC\right)}{area\left(\Delta DEF\right)}=\frac{B{C}^2}{E{F}^2}$

$\Rightarrow \frac{9}{16}=\frac{(2.1{)}^2}{E{F}^2}$

$\Rightarrow \frac{3}{4}=\frac{2.1}{EF}$

$\Rightarrow EF=\frac{4\times 2.1}{3}cm=2.8cm$