Question : If in $ riangle$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

Question

Question : If in $ riangle$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

Team Careers360 · Accepted Answer

Correct Answer: 10

Solution :
Given:
In $ riangle$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, $ riangle$ADE $\simeq riangle$ABC
$\frac{AD}{AB}=\frac{DE}{BC}$
⇒ $\frac{1.5}{7.5}=\frac{2}{BC}$
$ herefore BC=10$ cm
Hence, the correct answer is 10.

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Question : If in △ABC, DE || BC, AB = 7.5 cm, BD = 6 cm, and DE = 2 cm then the length of BC in cm is:Option 1: 6Option 2: 8Option 3: 10Option 4: 10.5

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Question : If in $△$ 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