SSC CGL 20 Aug 2021 Shift 2 Paper

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Question : 53 of 100

Marks: +1, -0

Points

P

and

Q

are on the sides

A B

and

B C

, respectively of a triangle

A B C

, right angled at

B

. If

A Q=11

{cm}, P C=8 {cm}

, and

A C=13 {cm}

, then find the length (in

{cm}

) of

P Q

.

$√{15}$
$4.5$
4
$4 √{7}$

Solution:

Given,

A C=13 {cm}, A Q=11 {cm}

,

P C=8 {cm}

We know that,

\;A C^{2}+P Q^{2}=A Q^{2}+P C^{2}

⇒\;(13)^{2}+P Q^{2}=(11)^{2}+(8)^{2}

⇒\;P Q^{2}=121+64-169

⇒\;P Q^{2}=16

∴ \;P Q=4 {cm}

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