CAT 2021 Slot 2 QA Question 20: Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that $AD : BD = 2 : 1$ and $AE : CE = 2 : 3$. If the area of the triangle ADE is 8 sq cm, then the area of the triangle

Question

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that $AD : BD = 2 : 1$ and $AE : CE = 2 : 3$. If the area of the triangle ADE is 8 sq cm, then the area of the triangle

Accepted Answer

Since D lies on AB and E lies on AC,

$\dfrac{AD}{AB}=\dfrac{2}{3}$
$\dfrac{AE}{AC}=\dfrac{2}{5}$

When two sides including the angle are scaled by these factors, the area is scaled by the product of the factors.
$\dfrac{[ADE]}{[ABC]}=\dfrac{AD}{AB} 	imes \dfrac{AE}{AC}$
$=\dfrac{2}{3} 	imes \dfra

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD:BD=2:1AD : BD = 2 : 1AD:BD=2:1 and AE:CE=2:3AE : CE = 2 : 3AE:CE=2:3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that $AD : BD = 2 : 1$ and $AE : CE = 2 : 3$ . If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is