cat 2021 Question 11

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 ABC, in sq cm, is

Accepted Answer

Now area of $ADE = \frac{1}{2} imes AD imes AE imes \sin A$

$= \frac{1}{2} imes 2x imes 2y imes \sin A = 8$

we get

$xy \sin A = 4$

Now area of triangle $ABC = \frac{1}{2} imes AB imes AC imes \sin A$

we get

$\frac{1}{2} imes 3x imes 5y imes \sin A = \frac{15}{2} xy \sin A = \frac{15}{2} imes 4$

We get area of ABC = 30

Question 11.

Question Explanation