SSC CGL 17 Aug 2021 Shift 3 Paper

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Question : 55 of 100

Marks: +1, -0

In

△ A B C, D

is a point on

B C

such that

B D: D C=3: 4 . E

is a point on

A D

such that

A E: E D=2: 3

. Find the ratio ar

(△ E C D): ar(△ A E B)

.

$9: 8$
$2: 1$
$1: 2$
$8: 9$

Solution:

Given, ratio,

B D: D C=3: 4

and

A E: E D=2: 3

We know that,
ratio of

\;{B D}/{D C}=\;{△ A D B}/{△ A D C}

So,

\;\; △ A E B=3 × \;{2}/{5}=\;{6}/{5}

and

△ E C D=4 × \;{3}/{5}=\;{12}/{5}

⇒ \;\; \;{△ E C D}/{△ A E B}=\;{\;{12}/{5}}/{{6}/{5}}=\;{2}/{1}

∴ △ E C D: △ A E B=2: 1

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