Question

If ΔABC ~ ΔDEF such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then perimeter of ΔABC is
A. 18 cm
B. 20 cm
C. 12 cm
D. 15 cm

Answer 1

Given :   ΔABC ~ ΔDEF, DE = 3 cm, BC = 4 cm , DF = 2.5 cm  , EF = 2 cm

Solution :

AB/DE = BC/EF = CA/FD  

[corresponding sides of two similar triangles are in proportional]

AB/DE = BC/EF

AB/3  = 4/2

AB/3 = 2/1

AB = 6 cm …………..(1)

Similarly ,  

BC/EF = CA/FD  

4/2 = CA/2.5

2 AC  = 4 × 2.5  

2 AC = 10

AC = 10/2

AC = 5 cm .. …………(2)

Perimeter of ∆ ABC = AB + BC + AC

= 6 + 4 + 5  

[From equation 1 and 2]

Perimeter of ∆ ABC = 15 cm

Hence, the Perimeter of ∆ABC is 15 cm.

Among the given options Option (d) 15 cm is the correct answer.

HOPE THIS ANSWER WILL HELP YOU……

 

Some more questions :  

If $\triangle ABC \sim \triangle DEF$ such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of $\triangle DEF$ is 25 cm, then the perimeter of $\triangle ABC$ is

(a) 36 cm

(b) 30 cm

(c) 34 cm

(d) 35 cm

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$\triangle ABC$ is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If $\triangle DEF \sim \triangle ABC$ and EF = 4 cm, then perimeter of $\triangle DEF$ is

(a) 7.5 cm

(b) 15 cm

(c) 22.5 cm

(d) 30 cm

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Answer 2

Answer:

option d) 15 cm.

Step-by-step explanation:

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