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 is
Answers
Answered by
12
Given :
A ∆ABC in which DE // BC. AD = 2cm, BD = 3 cm and BC = 7.5 cm.
To find :
The length of DE
_______________________________________
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.
Similar questions