Maths-
General
Easy

Question

The area of the equilateral triangle which containing three coins of unity radius is

  1. 6 plus 4 square root of 3   s q.   u n i t s    
  2. 8 plus square root of 3 sq. units    
  3. 4 plus fraction numerator 7 square root of 3 over denominator 2 end fraction sq. units    
  4. 12 plus 2 square root of 3sq. units    

The correct answer is: 6 plus 4 square root of 3   s q.   u n i t s


    In capital delta B C subscript 1 end subscript M; B M equals left parenthesis C subscript 1 end subscript M right parenthesis. cot invisible function application 3 0

    Þ B M equals square root of 3
    Þ Similarly, C N equals square root of 3and M N equals C subscript 1 end subscript C subscript 2 end subscript equals 1 plus 1 equals 2
    Hence, side B C equals square root of 3 plus square root of 3 plus 2 equals 2 left parenthesis 1 plus square root of 3 right parenthesis
    Þ Area of equilateral triangle
    equals fraction numerator square root of 3 over denominator 4 end fraction left square bracket 2 left parenthesis 1 plus square root of 3 right parenthesis right square bracket to the power of 2 end exponent=A B equals O A minus O B equals h left parenthesis cot invisible function application 1 5 to the power of o end exponent minus cot invisible function application 3 0 to the power of o end exponent right parenthesis sq units.

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