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D and E are points on sides AB and AC of triangle ABC such that DE is parallel to BC. If AD/AB = 1/4, the ratio of the area of triangle ADE to the area of triangle ABC is
A1 : 16
B1 : 8
C1 : 4
D4 : 1
Answer & Solution
Correct answer: A. 1 : 16
1. Triangles ADE and ABC are similar by AA (DE parallel to BC gives equal corresponding angles).
2. Side ratio AD : AB = 1 : 4.
3. Area ratio = square of side ratio = 1 : 16.
_Source: NCERT Class 10 Mathematics, Ch 6 "Triangles", §6.4_
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