Question

If ΔАВC ~ ΔDEF such that 2AB = DE and BC = 6 cm, find EF.

Answer 1

Given:

ΔABC ~ ΔDEF

2AB = DE

BC = 6 cm

Step-wise calculation:

1. From 2AB = DE, `(DE)/(AB) = 2`, so the linear scale factor from ΔABC to ΔDEF is 2.

2. For similar triangles corresponding sides are proportional, so `(AB)/(DE) = (BC)/(EF)`.

Hence, `(EF)/(BC) = (DE)/(AB)`.

3. Therefore, `EF = ((DE)/(AB)) xx BC`

= 2 × 6 cm

= 12 cm