Question : If in $\triangle$ABC, DE || BC, AB = 7.5 cm, BD = 6 cm, and DE = 2 cm then the length of BC in cm is:
Option 1: 6
Option 2: 8
Option 3: 10
Option 4: 10.5
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Correct Answer: 10
Solution :
Given:
In $\triangle$ABC, DE || BC, AB =7.5 cm, BD = 6 cm, and DE = 2 cm
So, AD = 7.5 – 6 = 1.5 cm
In ∆ ADE and ∆ ABC,
∵ DE | | BC
∵ $\angle$ADE = $\angle$B ; $\angle$AED = $\angle$C
∴ By AA - similarity,
Here, $\triangle$ADE $\simeq \triangle$ABC
$\frac{AD}{AB}=\frac{DE}{BC}$
⇒ $\frac{1.5}{7.5}=\frac{2}{BC}$
$\therefore BC=10$ cm
Hence, the correct answer is 10.
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