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In ΔABC, D and E are points on side AB and AC respectively. DE is parallel to BC. If lengths of AD, DB and DE are 8 cm, 6 cm and 4 cm respectively. What is the length of BC?

  1. 7 cm
  2. 4 cm
  3. 6 cm
  4. 10 cm

Answer (Detailed Solution Below)

Option 1 : 7 cm
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Detailed Solution

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Given

AD = 8 cm; DB = 6 cm; DE = 4 cm

Length of side AB = AD + DB = 8 + 6 = 14 cm

Property:

A line drawn parallel to any side, cuts the other two sides proportionally” gives us

⇒ AD/DE = AB/BC

⇒ 8/4 = 14/BC

⇒ BC = 14 × 4/ 8

⇒ BC = 56/8 = 7 cm

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