Question : If $\triangle A B C \sim \triangle F D E$ such that $A B=9 \mathrm{~cm}, A C=11 \mathrm{~cm}, D F=16 \mathrm{~cm}$ and $D E=12 \mathrm{~cm}$, then the length of $BC$ is:
Option 1: $5 \frac{3}{4} \mathrm{~cm}$
Option 2: $4\frac{3}{5} \mathrm{~cm}$
Option 3: $3\frac{5}{7} \mathrm{~cm}$
Option 4: $6\frac{3}{4} \mathrm{~cm}$
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Correct Answer: $6\frac{3}{4} \mathrm{~cm}$
Solution :
Given: $A B=9 \mathrm{~cm}, A C=11 \mathrm{~cm}, D F=16 \mathrm{~cm}$ and $D E=12 \mathrm{~cm}$
$\triangle ABC \sim \triangle FDE$
Now,
$\frac{AB}{DF}= \frac{BC}{DE}$
Substituting the given values:
⇒ $\frac{9}{16}= \frac{BC}{12}$
$⇒BC = 12 \times \frac{9}{16} = 6\frac{3}{4} \mathrm{~cm}$
Hence, the correct answer is $6\frac{3}{4} \mathrm{~cm}$.
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