If $\triangle A B C \sim \triangle E D F$ such that AB = 6 cm, DF = 16 cm and DE = 8 cm, then the length of BC is :

12 cm

Concept Used

When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Calculations

As \(\Delta \)ABC is similar to \(\Delta \)EDF

So, \(\frac{AB}{DE}\) = \(\frac{AC}{FE}\)

Now,

\(\frac{AB}{DE}\) = \(\frac{BC}{DF}\)

= \(\frac{6}{8}\) = \(\frac{BC}{16}\)

= BC = \(\frac{6 \;×\;16 }{8}\)

= BC = \(\frac{96}{8}\)

= BC = 12 cm

Therefore, BC is 12 cm.