Question

2. In the figure AB, CD and EF are parallel. PC = 6 cm CE = 3 cm Find DF and PF​

Answer 1

Answer:

x=5cm

Step-by-step explanation:

Correct option is B)

In △BCD and △BEF,

∠DBC=∠FBE (Common angle)

∠BCD=∠BEF (Corresponding angles of parallel lines CD and EF)

∠BDC=∠BFE (Corresponding angles of parallel lines CD and EF)

Thus, △BCD∼△BEF (AAA rule)

Hence,  

BE

BC

​

=  

BF

BD

​

=  

EF

CD

​

 (Corresponding sides)

x+3

x

​

=  

BF

BD

​

=  

4.5

y

​

 ..(I)

Similarly, △FCD∼△FAB

Thus,  

FA

FC

​

=  

AB

CD

​

=  

FB

FD

​

 

7.5

y

​

=  

BF

DF

​

 (II)

From I and II,

BD=  

4.5

y

​

BF and DF=  

7.5

y

​

BF

BD+DF=BF

4.5

y

​

BF+  

7.5

y

​

BF=BF

7.5y+4.5y=7.5×4.5

y=  

16

45

​

 

Also,  

x+3

x

​

=  

4.5

y

​

 

x+3

x

​

=  

16×4.5

45

​

 

x+3

x

​

=  

72

45

​

 

72x=45x+135

27x=135

x=5cm