Question

in the adjoining figure,if AD=5cm,BD=7,AC=18cm and BD parallel toDE,then find CE
​

Answer 1

Answer: The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that DE∣∣AB,AD=7 cm, CD=5 cm and BC=18 cm.

Using the basic proportionality theorem, we have

CA

CD

​  

=  

AB

DE

​  

=  

CB

CE

​  

 

⇒  

CA

CD

​  

=  

CB

CE

​  

 

⇒  

12

5

​  

=  

18

CE

​  

 

⇒18×5=12CE

⇒12CE=90

⇒CE=  

12

90

​  

=7.5

Since CE=7.5 cm, therefore,

CB=CE+EB

⇒18=7.5+EB

⇒EB=18−7.5=10.5

Hence, BE=10.5 cm and CE=7.5 cm.