SSC CGL 17 Aug 2017 Shift 2 Paper

Question : 68 of 100

Marks: +1, -0

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD : DB = 2:5 and area of ΔADE is 8 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

(4:45)
(45:4)
(8:45)
(45:8)

Validate

Solution:

According to the question,

∵

D E ∥ B C

\Δ A D E∼ \Δ A B C, A D: D B=2: 5

{ { \Area \of } \Δ A D E}/{ { \Area \of } \ΔA B C}= ( {A D}/{A B} )^{2}

⇒

{8/{ { \Area \of } \ΔA B C}= ( {2}/{7} )^{2}

∴

Area of

\Δ A B C = {8 ×49}/{4}=98 {\cm}^{2}

∴ Area of quadrilateral BDCE = Area of ΔABC - Area of ΔADE

= 98 - 8 = 90 \cm^2

Hence, required ratio

={{ \Area \of } \Δ A D E}/{\Area \of \quadrilateral \BDEC}

= {8}/{90}=4: 45

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