SSC CGL 18 Aug 2021 Shift 3 Paper

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Question : 59 of 100

Marks: +1, -0

What is the length (in

{cm}

) of the smallest altitude of the triangle whose sides are

5 {cm}, 12 {cm}, 13 {cm}

? (correct to one decimal place)

$12.0$
$5.1$
$2.6$
$4.6$

Solution:

Given,

a=5 {cm}, b=12 {cm}

,

c=13 {cm}

S \;\; =\;{a+b+c}/{2}=\;{5+12+13}/{2}

\;\; =\;{30}/{2}=15 {cm}

Area of triangle

\;\; =√{S(S-a)(S-b)(S-c)}

\;\; =√{15(15-5)(15-12)(15-13)}

\;\; =√{15 × 10 × 3 × 2}

\;\; =√{3 × 5 × 5 × 2 × 3 × 2}

\;\; =3 × 5 × 2=30 {cm}^{2}

We know that,

\;\text " Area of triangle "\;=\;{1}/{2} × b × h

⇒ \;\; 30=\;{1}/{2} × 13 × h

⇒ \;\; \;{60}/{13}=\;\text " height "\;

∴ \;\text " Height "\;=4.6 {cm}

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