Question

∆ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ∆DEF ∼ ∆ABC and EF = 4 cm, then perimeter of ∆DEF is

Options

• 7.5 cm

• 15 cm

• 22.5 cm

• 30 cm

Answer 1

Given: In ΔABC, AB = 3cm, BC = 2cm, CA = 2.5cm. `ΔDEF ∼ Δ ABC ` and EF = 4cm.

To find: Perimeter of ΔDEF.

We know that if two triangles are similar, then their sides are proportional

Since ΔABC and ΔDEF are similar,

`(AB)/(DE)=(BC)/(EF)=(CA)/(FD)`

`3/(DE)=2/4=2.5/(FD)`

`3/(DE)=2/4`...............(1)

`DE=6cm`

`2/4=2.5/(FD)`

`FD=5cm......................(2)

From (1) and (2), we get

Perimeter of ΔDEF =  DE + EF + FD = 6 + 4 +5 = 15 cm

Hence the correct answer is `b`