SSC CGL 17 Aug 2021 Shift 1 Paper

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Question : 51 of 100

Marks: +1, -0

In

△ A B C, D

and

E

are the points on the sides

A B

and

A C

, respectively and

D E \| B C . B C=8

{cm}

and

D E=5 {cm}

. If the area of

△ A D E=45 {cm}^{2}

, then what is the area (in

{cm}^{2}

) of

△ A B C

?

$115.2$
$105.2$
125
64

Solution:

Given,

B C=8 {cm}, D E=5 {cm}

ar(△ A D E)=45 {cm}^{2}

,

We know that,

\;{ar(△ A B C)}/{ar(△ A D E)}=(\;{B C}/{D E})^{2}

⇒ \;\; \;{ar(△ A B C)}/{ar(△ A D E)}=\;{64}/{25}

⇒ \;\; ar(△ A B C)=64 × \;{45}/{25}=64 × \;{9}/{5}

\;\; [ ∵ ar(△ A D E)=45]

⇒ ar(△ A B C)=115.2 {cm}^{2} .

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