Question

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D and E are respectively the points on the side a b and a c of a triangle ABC such that ad = 3 cm,BD=5 cm BC= 12.8 cm and DE || BC.The length of the DE is​

Answer 1

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. Hence,BD = 3.6 cm and CE = 4.8 cm. This discussion on 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.

Answer 2

Answer: DE = 4.8 cm

Explanation:

In ∆ADE & ∆ABC,

• ∠ADE = ∠ABC
• ∠AED = ∠ACB

(Alternate interior angles are same.)

Therefore, ∆ADE ~ ∆ABC (by AA criterion).

It implies that:

AD/AB = DE/BC

=> 3/8 = DE/12.8

=> DE = 3/8 × 12.8 = 4.8 cm