Xavier Aptitude Test 2016 Paper

Question : 58 of 103

Marks: +1, -0

The difference between the area of the circumscribed circle and the area of the inscribed circle of an equilateral triangle is 2156 sq cm. What is the area of the equilateral triangle?

686 $√3$
1000
961 $√2$
650 $√3$
None of the above

Validate

Solution:

(a) Let side of equilateral triangle be x cm

\∴ \

circum Radius

=\ {\ {x}}/{\√{3}}

In Radius =

\ {\ {x}}/{2 \√{3}}

\∴\

Area of circumscribed circle

=\π(\ {\ {x}}/{\√{3}} )^{2} \ .........

(1)
Area of In-scribed circle

=\π ( { {x}}/{2 \√{3}}\ )^{2}

∴ \ π( {\ {x}}/{\√{3}}\ )^{2}-\π(\ {\ {x}}/{2 \√{3}} )^{2}=2156

\ {π{x}^{2}}/{3}-\ {\π{x}^{2}}/{4 × 3}=2156

\ {4 \π x^{2}-\π x^{2}}/{12}=2156

\ {3 \π x^{2}}/{12}=2156

x^{2}=\ {2156 ×12 × 7}/{3 \× 22}

x^{2}=98 \× 4 \× 7

\ ......(1)

Area of equilateral triangle =

\ {\√{3}}/{4} x^{2}

=\ {√{3}}{4} \× 98× 4 × 7

=686 \√{3}

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