Question

Parth went to Coorg on a holiday. He wanted to make a tent using a canvas cloth and a few bamboo sticks as support. Initially, he made a sketch of the tent as shown in the figure. He wanted to make the tent as an exact replica of the sketch. So, he placed the bamboo stick DE parallel to the ground BC and AG perpendicular to the ground. Let’s analyse his sketch.


In his sketch, $\frac{Areaof\Delta ADE}{Areaof\Delta ABC}=$

[1 mark]

• A. $\frac{4}{25}$
• B. $\frac{25}{4}$
• C. $\frac{25}{9}$
• D. $\frac{9}{25}$

Answer 1

The correct option is A $\frac{4}{25}$

$\Delta ADEand\Delta ABC$ are similar triangles.

$\frac{Areaof\Delta ADE}{Areaof\Delta ABC}=(Ratioofcorrespondingsides{)}^2$

We have, $\frac{AD}{DB}=\frac{2}{3}\Rightarrow$ $\frac{DB}{AD}=\frac{3}{2}$

$\Rightarrow \frac{AD+DB}{AD}=\frac{3+2}{2}$

$\Rightarrow \frac{AB}{AD}=\frac{5}{2}\Rightarrow \frac{AD}{AB}=\frac{2}{5}$

$\frac{Areaof\Delta ADE}{Areaof\Delta ABC}={\left(\frac{AD}{AB}\right)}^2={\left(\frac{2}{5}\right)}^2=\frac{4}{25}$