In a triangle ABC, D & E are the points on AB & AC respectively such that DE is parallel to AC & AD : AB = 3 : 8, then (area of ADE) : ( area of quad DEBC) is :
Show answer & explanation
Correct answer: A
Explanation
Note: The question has been modified since it was incorrect according to the answer key released by SSC
The correct answer is option 1 i.e 9 : 55
Given, AD : AB = 3 : 8
As triangle ADE is similar to triangle ABC,
by the property of similar triangles,
(AD: AB)2 = area (triangle ADE) / area (triangle ABC)
⇒ 9 : 64 = area( triangle ADE) / area (triangle ABC)
From this, area of quadrilateral (DEBC) = 64 - 9 = 55
Hence,
Area of the triangle (ADE) / Area of quadrilateral (DEBC) = 9: 55