D and E are respectively the points on the sides AB and AC on the triangle ABC such that AD=2cm, BD=3cm, BC=7.5cm and DE||BC. Then length of DE (in cm) is....
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Answer:
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.
Step-by-step explanation:
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