SSC CGL 24 Aug 2021 Shift 3 Paper

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Question : 67 of 100

Marks: +1, -0

△ A B C

is right angled at

B . B D

is an altitude intersecting

A C

at

D

. If

A C=9 {cm}

and

C D=3 {cm}

, then find the measure of

A B

(in

{cm}

).

$3 √{6}$
3
$6 √{3}$
6

Solution:

Given,

A C=9 {cm}, C D=3 {cm}

then,

A D=A C-C D=9-3=6 {cm}

In

△ A B C

and

△ A D B

,

\;∠ A B C \;\; =∠ A D B=90^{∘}

\;∠ B A C \;\; =∠ D A C \;\; \;\text " (common angles) "\;

∴ \;\;{A C}/{A B} \;\; =\;{A B}/{A D}

⇒\;\;{9}/{A B} \;\; =\;{A B}/{6}

⇒\;A B^{2} \;\; =9 × 6

∴ \;A B \;\; =3 √{6} {cm}

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