## 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

Question

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## Answers ( )

Given :

A ∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.

To find :

The length of DE

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Since, DE is parallel to BC

→ angle ADE = angle ABC (corresponding angles)

→ angle AED = angle ACB (corresponding angles)

Hence, by AA criterion of similarity,

∆ADE ~ ∆ABC

ratio of corresponding sides of similar triangles are equal.

AD/AB = DE/BC

AB = AD + DB

AB = 2 + 3 = 5 cm

So,

2/5 = DE/7.5

DE = 2/5 × 7.5

DE = 2 × 1.5

DE = 3 cm.

Hence, the length of side DE is 3 cm.