In the given figure we have been given the length of sides AO=10 cm,OC=5 cm,AB=6.5 cm and OD=2.8 cm and we are to

(i) Prove that △OAB∼△OCD.

(ii) Find CD and OB

(iii) Calculate the ratio of areas of △OAB and △OCD

ML Aggarwal, Avichal Publication, class 10, Similarity, chapter 13.3, question no 5b

## From the question it is given that,

AB∥DC.AO=10cm,OC=5cm,AB=6.5cm and OD=2.8cm

(i) We have to prove that, △OAB∼△OCD

So, consider the △OAB and △OCD

∠AOB=∠COD … [because vertically opposite angles are equal]

∠OBA=∠OCD … [because alternate angles are equal]

Therefore, △OAB∼△OCD … [from AAA axiom]

(ii) Consider the △OAB and △OCD

OA/OC=OB/OD=AB/CD

Now consider OA/OC=OB/OD

10/5=OB/2.8

OB=(10×2.8)/5

OB=2×2.8

OB=5.6cm

Then, consider OA/OC=AB/CD

10/5=6.5/CD

CD=(6.5×5)/10

CD=32.5/10

CD=3.25cm

(iii) We have to find the ratio of areas of △OAB and △OCD.

From (i) we proved that, △OAB∼△OCD

Then, area of (△OAB)/area of △OCD

AB2/CD2=(6.5)2/(3.25)2

=(6.5×6.5)/(3.25×3.25)

=2×2/1

=4/1

Therefore, the ratio of areas of △OAB and △OCD=4:1.