Question

If ∆ ABC and ∆ DEF are similar such that 2AB = DE and BC = 8 cm, then EF = ______.

Options

• 16 cm

• 12 cm

• 8 cm

• 4 cm

Answer 1

If ∆ ABC and ∆ DEF are similar such that 2AB = DE and BC = 8 cm, then EF = 16 cm.

Explanation:

Given: 2AB = DE

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

BC = 8 cm

To find: EF = ?

When two triangles are similar (Δ ABC ∼ Δ DEF), their corresponding sides are proportional. 

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

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

`1/2 = 8/(EF)`

1 × EF = 8 × 2

EF = 16 cm