SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 82 of 100

Marks: +1, -0

D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD : DB = 4 : 5, CD and BE intersect each other at F. Then find the ratio of the areas of ΔDEF and ΔCBF.

16 : 25
16 : 81
81 : 16
4 : 9

Validate

Solution:

(2)

DE || BC
∠ADE = ∠ABC
∠AED = ∠ACB
By AA–similarity.
DABC ~ DADE

∴{ {AD}}/{ {AB}}= {\ {DE}}/{ {BC}}

∴{ {AD}}/{ {DB}}= {4}/{5}

⇒{ {DB}}/{ {AB}}= {5}/{4}

⇒{ {DB}+ {AD}}/{ {AD}}= {5+4}/{4}

⇒{A B}/{A D}= {9}/{4}= {B C}/{D E}

\Δ D E F ~\Δ C B F

∴{ { \Area \of } \Δ{DEF}}/{ { \Area \of } \Δ {CBF}}= { {DE}^{2}}/{ {BC}^{2}}=16/81

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