Question

If ΔАВС ~ ΔDEF, DE = 6 cm, EF = 9 cm, FD = 12 cm and AB = 3 cm, then find the perimeter of ΔAВС.

Answer 1

Given:

△ABC ∼ △DEF and DE = 6 cm, EF = 9 cm, FD = 12 cm, AB = 3 cm

Since △ABC ∼ △DEF, the corresponding sides are:

AB ↔ DE, BC ↔ EF, AC ↔ FD

So the scale factor from △DEF to △ABC is:

`(AB)/(DE) = 3/6 = 1/2`

Now let’s find the other sides of △ABC:

⇒ `BC = 1/2 xx EF`

`BC = 1/2 xx 9`

∴ BC = 4.5 cm

⇒ `AC = 1/2 xx FD`

`AC = 1/2 xx 12`

∴ AC = 6 cm

Perimeter of △ABC:

AB + BC + AC = 3 + 4.5 + 6

∴ Perimeter of △ABC = 13.5 cm