Question

If ∆ABC ∼ ∆DEF such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then perimeter of ∆ABC is 

विकल्प

•  18 cm

• 20 cm

• 12 cm

• 15 cm

Answer 1

Given: ΔABC and ΔDEF are similar triangles such that DE = 3cm, EF = 2cm, DF = 2.5cm and BC = 4cm.

To find: Perimeter of ΔABC.

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

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

Substituting the values we get

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

`(AB)/4=3/2`

`AB=6cm`..................(1)

Similarly,

`(CA)/(BE)=(DF)/(EF)`

`(CA)/4=2.5/2`

`CA=5cm`

Perimeter of Δ ABC = AB+BC+CA 

= 6+4+5

= 15 cm

Hence the correct option is `d`