Question

If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ABC.

Answer 1

According to the question,

AB = 4 cm,

DE = 6 cm

EF = 9 cm

FD = 12 cm

Also,

∆ABC ∼ ∆DEF

We have,

∴ `("AB")/("ED") = ("BC")/("EF") = ("AC")/("DF")`

⇒ `4/6 = ("BC")/9 = ("AC")/12`

By taking first two terms, we have

⇒ `4/6 = ("BC")/9`

⇒ BC = `((4 xx 9))/6` = 6 cm

And by taking last two terms, we have,

`("BC")/9 = ("AC")/12`

`6/9 = ("AC")/12`

AC = `(6 xx 12)/9` = 8 cm

Now,

Perimeter of ∆ABC

= AB + BC + AC

= 4 + 6 + 8

= 18 cm

Thus, the perimeter of the triangle is 18 cm.