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Question

# An equilateral triangle and a regular hexagon have the same perimeter. If the area of the hexagon is 72√3, calculate the area of the triangle.

A
62.354
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B
83.138
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C
101.823
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D
103.923
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E
124.708
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Solution

## The correct option is A 83.138Let the length of side of equilateral triangle be a and the length of side of hexagon be b.Given, 3a=6b , which implies a=2bArea of hexagon is 6×12×b×b×sin(60)=3√32b2=72√3 , which impliesb2=48 ⇒b=4√3therefore a=2b=8√3Area of equilateral triangle is 12×a×a×sin60=√34a2=√34×64×3=48√3=83.138

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