Question

If $\triangle ABC and \triangle DEF$ are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, write the perimeter of $\triangle DEF$ .

Answer 1

Answer:

The Perimeter of ∆ DEF is 15 cm.

Step-by-step explanation:

Given :  

ΔABC ~ ΔDEF, AB = 3 cm, BC = 2 cm , CA = 2.5 cm  , EF = 4cm

AB/DE = BC/EF = CA/FD  

[corresponding sides of two similar triangles are in proportional]

AB/DE = BC/EF

3/DE = 2/4

2 DE = 3 × 4  

2 DE = 12

DE = 12/2  

DE = 6 cm …………..(1)

 

Similarly ,  

BC/EF = CA/FD  

2/4 = 2.5/FD

2 FD = 4 × 2.5  

2 FD = 10

FD = 10/2

FD = 5 cm .. …………(2)

Perimeter of ∆ DEF = DE + EF + FD

= 6 + 4 + 5  

[From equation 1 and 2]

Perimeter of ∆ DEF = 15 cm

Hence, the Perimeter of ∆ DEF is 15 cm.

HOPE THIS ANSWER WILL HELP YOU ..

 

Answer 2

ANSWER in attatchment................