Question : In $ riangle ext{ABC}, \mathrm{DE} \| \mathrm{BC}$ and $\frac{ ext{AD}}{ ext{DB}}=\frac{4}{5}$. If $\mathrm{DE}=12 \mathrm{~cm}$, find the length of $\mathrm{BC}$.
Option 1: 48 cm
Option 2: 12 cm
Option 3: 30 cm
Option 4: 27 cm

Question

Question : In $ riangle ext{ABC}, \mathrm{DE} \| \mathrm{BC}$ and $\frac{ ext{AD}}{ ext{DB}}=\frac{4}{5}$. If $\mathrm{DE}=12 \mathrm{~cm}$, find the length of $\mathrm{BC}$.

Option 1: 48 cm

Option 2: 12 cm

Option 3: 30 cm

Option 4: 27 cm

Team Careers360 · Accepted Answer

Correct Answer: 27 cm

Solution :
According to the question,
$\mathrm{DE} \| \mathrm{BC}$
$\frac{ ext{AD}}{ ext{DB}}=\frac{4}{5}$
DE = 12 cm
By the SAS criterion of similarity, we have
△ABC $\sim$ △ADE
$ herefore$ $\frac{ ext{AB}}{ ext{AD}} = \frac{ ext{BC}}{ ext{DE}}$
⇒ $ ext{BC} = \frac{ ext{AB}}{ ext{AD}} imes ext{DE}$
⇒ $ ext{BC} = \frac{ ext{AD+DB}}{ ext{AD}} imes 12$
⇒ $ ext{BC} = (1+\frac{ ext{DB}}{ ext{AD}}) imes 12$
⇒ $ ext{BC}=12 imes(1+\frac{5}{4}) = 3 imes 9 = 27$ cm
Hence, the correct answer is 27 cm.

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Question : In △ABC,DE‖BC and ADDB=45. If DE=12 cm, find the length of BC.Option 1: 48 cmOption 2: 12 cmOption 3: 30 cmOption 4: 27 cm

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Question : In $△ ABC, DE ‖ BC$ and $\frac{AD}{DB} = \frac{4}{5}$ . If $DE = 12 cm$ , find the length of $BC$ .
Option 1: 48 cm
Option 2: 12 cm
Option 3: 30 cm
Option 4: 27 cm