Question

In a ∆ABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm, find BD and CE.

Answer 1

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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Answer 2

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