Question

In triangle ABC, D is a point on AB, E is a point on AC and DE || BC. If AD: DB = 5:4, find :
( ) DE, if BC = 27 cm
(ii) ar (DADE): ar (DABC)
(iii) ar (DADE): ar (trapezium DBCE)​

Answer 1

Answer:

Explanation:

DE∥BC            [ Given ]

Let AD=5x and DB=4x

Then, AB=AD+DB=5x+4x=9x

In △ADE and △ABC

⇒  ∠ADE=∠ABC             [ Corresponding angles ]

⇒  ∠A=∠A        [ Common angle ]

∴  △ADE∼△ABC             [ By AA similarity rule ]

⇒    

AB

AD

​

=  

BC

DE

​

                 [ CPCT ]

⇒    

9x

5x

​

=  

BC

DE

​

   

BC

DE

​

=  

9

5

​

               ----- ( 1 )

Now, In △DEF and △CFB

⇒  ∠EDF=∠BCF                 [ Alternate angles ]

⇒  ∠DFE=∠CFB            [ Vertically opposite angles ]

⇒  △DFE∼△CFB     [ AA similarity rule ]

⇒    

ar(△CFB)

ar(△DFE)

​

=  

BC  

2

 

DE  

2

 

​

 

                           

 =  

(9)  

2

 

(5)  

2

 

​

 

 =  

81

25

​