D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD : DB = 5 : 4, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 25 : 81.
D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and
AD : DB = 5 : 4, CD and BE intersect each other at F.
If two triangles are similar:
Ratio of areas of two triangles = Ratio of squares of corresponding sides.
Triangles ABC and ADE:
DE || BC
So, these two triangles are similar triangles.
Now,
AD/AB = DE/BC
⇒ 5/(5 + 4) = DE/BC
⇒ DE/BC = 5/9
Now,
Triangles DEF and BCF are also similar.
So,
Area of DEF : Area of BFC = DE2 : BC2
⇒ 52 : 92
⇒ 25 : 81