SSC CHSL 12 Oct 2020 Shift 3 Paper

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Question : 57 of 100

Marks: +1, -0

If the three sides of a triangle are

11 {\cm}, 12 {\cm}

and

13 {\cm}

, then what is the area of the given triangle (in

{\cm}^{2}

)?

$13 \√{26}$
$15 \√{13}$
$6 \√{105}$
$17 \√{42}$

Solution:

Sides of triangle,

a=11 {\cm}

,

b=12 {\cm}, c=13 {\cm}

Semi perimeter

(s)={a+b+c}/{2}

={11+12+13}/{2}

={36}/{2}=18 {\cm}

Area of triangle

=\√{s(s-a)(s-b)(s-c)}

=\√{18 \×(18-11) \×(18-12) \×(18-13)}

=\√{18 \×7 \× 6 \×5}

=\√{6 \×3 \×7 \×6 \×5}

=6 \√{105} {\cm}^{2}

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