Question

Is it possible to construct triangles with measures as given below?

(i) ΔDEF with DE = 3 cm, EF = 30 cm, DF = 32 cm
(ii) ΔPQR with PQ = 30 cm, QR = 2 cm, PR = 20 cm

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