SSC CGL 18 Aug 2021 Shift 2 Paper

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Question : 74 of 100

Marks: +1, -0

△ A B C ∼ △ D E F

. If the areas of

△ A B C

and

△ D E F

are

100 {cm}^{2}

and

81 {cm}^{2}

, respectively and the altitude of

△ D E F

is

6.3 {cm}

, then the corresponding altitude of

△ A B C

is

$9 {cm}$
$5.6 {cm}$
$7 {cm}$
$8.4 {cm}$

Solution:

Given,

△ A B C ∼ △ D E F

We know that,

\;{\;\text " Area of "\; △ A B C}/{\;\text " Area of "\; △ D E F}=(\;{\;\text " side of "\; △ A B C}/{\;\text " side of "\; △ D E F})^{2}

⇒ \;\; √{\;{100}/{81}}=\;{h}/{6.3}

⇒ \;\; \;{10}/{9}=\;{h}/{6.3}

∴ \;\; h=\;{63}/{9}=7 {cm}

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