Question

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

Answer:

Given :

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

To find :-

• The length of DE

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Since, DE is parallel to BC

$\sf \: → \angle \: ADE = \angle \: ABC \: \: (corresponding \: \: angles)$

$\sf→ \sf \: \angle \: AED = \angle \: ACB \: \: (corresponding \: angles)$

Hence, by AA criterion of similarity,

∆ADE ~ ∆ABC

ratio of corresponding sides of similar triangles are equal.

$\sf \: \frac{AD}{AB} = \frac{DE}{BC} \\ \\ \sf \: AB = AD + DB$

AB = 2 + 3 = 5 cm

So,

$\\ \sf \frac{2}{5} = \frac{DE}{7.5}\\ \\ \sf \: DE = \frac{2}{5} × 7.5$

DE = 2 × 1.5

DE = 3 cm.

Hence, the length of side DE is 3 cm