SSC CGL 12 Aug 2017 Shift 1 Paper

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Question : 68 of 100

Marks: +1, -0

If sum of the areas of the circumcircle and the incircle of an equilateral triangle is

770 {\cm}^{2}

then what is the area (in

{\cm}^{2}

) of the triangle?

$125 √{3}$
$147√{3}$
$156 √{3}$
$169 √{3}$

Solution:

Circumradius

= {a}/{√{3}}

Inradius

= {a}/{2 √ {3}}

According to the question,

\π[ {a}/{√{3}} ]^{2}+\π[ {a}/{2 √{3}} ]^{2}=770

⇒

\π[ {a^{2}}/{3}+ {a^{2}}/{12} ]=770

= {4 a^{2}+a^{2}}/{12}= {770 ×7}/{22}

⇒

5 a^{2}= {70 × 7 × 12}/{2}

∴

a^{2}=588

Area of equilateral triangle

= {√{3}}/{4} a^{2}= {√{3}}/{4} × 588

=147√{3} {\cm}^{2}

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