Question

In $\Delta ABC\Delta DEF,\angle A=\angle D,\angle B=\angle E$ Find $\frac{area\Delta ABC}{area\Delta DEF}$ is DE = 20cm and AB = 16 cm

• A. $\frac{16}{25}$
• B. $\frac{25}{16}$
• C. $\frac{5}{4}$
• D. $\frac{\sqrt{5}}{2}$

Answer 1

The correct option is A $\frac{16}{25}$

$\Delta ABCsim\Delta DEFbyAAA$
So, $\Delta ABCsim\Delta DEF⟹\frac{areaof\Delta ABC}{areaof\Delta DEF}={\left(\frac{AB}{DE}\right)}^2⟹\frac{areaof\Delta ABC}{areaof\Delta DEF}={\left(\frac{16}{20}\right)}^2=\frac{16}{25}$