Question

If $\triangle ABC \sim \triangle DEF$ such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then perimeter of $\triangle ABC$ is
(a) 18 cm
(b) 20 cm
(c) 12 cm
(d) 15 cm

Answer 1

Answer:

The Perimeter of ∆ABC is 15 cm.

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

Step-by-step explanation:

Given :  

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

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.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Answer:

such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then perimeter of. is (a) 18 cm.