Q. 234.3( 3 Votes )

# In the given figu

Answer :

We have MN || BC,

So, AMN = B and ANM = C (Corresponding angles)

We know that if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar (AA criteria).

ΔAMN ~ ΔABC.

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

i.e. ar(ΔAMN)/ ar(ΔABC) = (AM/AB)2

Given that AM: MB = 1: 2.

Since AB = AM + MB,

AB = 1 + 2 = 3.

ar(ΔAMN)/ ar(ΔABC) = (1/3)2

ar(ΔAMN)/ ar(ΔABC) = 1/9

area(ΔAMN)/ area(ΔABC) = 1/9

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Quiz- Test what you Know45 mins  Quiz- Test what you Know Part 245 mins  Similarity - Apply it like a Champ45 mins  BPT ke Master Kaise Bane?46 mins  Pythagoras Theorem ki Application46 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

<img width=RD Sharma - Mathematics

<img width=RD Sharma - Mathematics

If <img widRD Sharma - Mathematics

The areas of two RD Sharma - Mathematics

The areas of two RD Sharma - Mathematics

In Fig. 4.236, <sRD Sharma - Mathematics

If <img widRD Sharma - Mathematics

If the altitude oRD Sharma - Mathematics

If the areas of tRD Sharma - Mathematics