Question

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

पर्याय

• 28 cm

• 28.5 cm

• 18 cm

• 23 cm

Answer 1

If ∆ABC ~ ∆DEF, AB = 6 cm, DE = 9 cm, EF = 6 cm and FD = 12 cm, then the perimeter of ∆ABC is 18 cm.

Explanation:

Since ∆ABC ~ ∆DEF

We have the ratio of corresponding sides:

`(AB)/(DE) = (BC)/(EF) = (AC)/(DF) = ("Perimeter of" ∆ABC)/("Perimeter of" ∆DEF)`

Given, AB = 6 cm, DE = 9 cm, EF = 6 cm, FD = 12 cm

Perimeter of ∆DEF = DE + EF + DF

= 9 + 6 + 12

= 27

Now use the side ratio:

`(AB)/(DE) = 6/9 = 2/3`

So the ratio of perimeters is also:

`("Perimeter of" ∆ABC)/27 = 2/3`

Cross-multiply:

Perimeter of ∆ABC = `2/3 xx 27` 

= 9 × 2

= 18 cm