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D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE || BC. Then length of DE (in cm) is
  • a)
    4.8 cm
  • b)
    7.6 cm
  • c)
    19.2 cm
  • d)
    2.5 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
D and E are respectively the points on the sides AB and AC of a triang...
GIVEN: In  Δ ABC, D and E are points on AB and AC , DE ||  BC and  AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BE = 5 cm.
In Δ ADE and Δ ABC,
∠ADE =∠ABC    (corresponding angles)
[DE || BC, AB is transversal]
∠AED =∠ACB     (corresponding angles)
[DE || BC, AC is transversal]
So, Δ ADE  ~ Δ ABC      (AA similarity)
Therefore, AD/AB = AE/AC = DE/BC
[In similar triangles corresponding sides are proportional]
AD/AB = DE/BC
2.4/(2.4+DB)  = 2/5
2.4 × 5  = 2(2.4+ DB)
12 = 4.8 + 2DB
12 - 4.8  = 2DB
7.2 = 2DB
DB = 7.2/2  
DB = 3.6 cm
Similarly, AE/AC = DE/BC
3.2/(3.2+EC) = 2/5
3.2 × 5 = 2(3.2+EC)
16 = 6.4 + 2EC
16 - 6.4 = 2EC
9.6 = 2EC
EC = 9.6/2
EC = 4.8 cm
Hence,BD = 3.6 cm and CE = 4.8 cm.
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D and E are respectively the points on the sides AB and AC of a triang...
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So, the Correct Answer is Option A

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D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 3 cm, BD = 5 cm, BC = 12.8 cm and DE || BC. Then length of DE (in cm) isa)4.8 cmb)7.6 cmc)19.2 cmd)2.5 cmCorrect answer is option 'A'. Can you explain this answer?
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