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 :
Answer & explanation
Correct answer: option 1
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.