Q. 184.8( 4 Votes )

In a trapezium AB

Answer :

2.jpg


Let us consider AOB and COD.


AOB = COD ( vertically opposite angles)


OBA = ODC ( alternate interior angles)


OAB = OCD ( alternate interior angles)


We know that if in two triangles, corresponding angles are equal,


then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar (AAA criteria).


So, ΔAOB ΔCOD.


Given, AB = 2CD and ar(ΔAOB) = 84 cm2


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


ar(AOB)/ar(COD) = (AB/CD)2


84cm2/ar(ΔCOD) = (2CD/CD)2


84cm2/ar(ΔCOD) = 4


ar(ΔCOD) = 84cm2/4


ar(ΔCOD) = 21cm2


ar(ΔCOD) = 21cm2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
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