Question

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

Answer 1

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.