Question

3) The perimeters of two similar triangles
30 cm and 20 cm respectively. If a side
the first triangle is 12 cm then find the
corresponding side of the second triangle
(1) 5 cm (2) 10 cm (3) 22 cm
(4) 8cm​

Answer 1

Answer:

Step-by-step explanation:

Let △ABC and △DEF be two similar triangles of perimeters P  

1

​  

 and P  

2

​  

 respectively.

Also, let AB=12 cm, P  

1

​  

=30 cm and P  

2

​  

=20 cm.

 

Then,

 

DE

AB

​  

=  

EF

BC

​  

=  

DF

AC

​  

=  

P  

2

​  

 

P  

1

​  

 

​  

  [∵ Ration of corresponding sides of similar triangles is equal to the ratio of their perimeters]

⇒    

DE

AB

​  

=  

P  

2

​  

 

P  

1

​  

 

​  

 

⇒    

DE

12

​  

=  

20

30

​  

 

⇒  DE=  

30

12×20

​  

cm=8cm

Hence, the corresponding side of the second triangle is 8 cm