ΔABC is such that AB=3cm, BC=2cm, CA=2.5cm. If . . .

Question : ΔABC is such that AB=3cm, BC=2cm, CA=2.5cm. If ΔABC~ΔDEF and EF=4cm, then perimeter of ΔDEF is 

a) 7.5 cm

b) 15 cm

c) 22.5 cm

d) 30 cm

Doubt by Mehak

Solution : 

Using Perimeter of similar Triangle Theorem

According to this theorem, the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

ΔABC~ΔDEF (Given)

Perimeter of ΔABC / Perimeter of ΔDEF = BC/EF

(AB+BC+CA) / Perimeter of ΔDEF = BC/EF
(3+2+2.5) / Perimeter of ΔDEF = 2/4
7.5 / Perimeter of ΔDEF = 1/2
Perimeter of ΔDEF = 7.5×2

Perimeter of ΔDEF = 15 cm

Hence, b) 15 cm would be the correct option.