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n triangle A B C comma blankifblank r subscript 1 end subscript equals 2 r subscript 2 end subscript equals 3 r subscript 3 end subscript comma thenblank a colon b is equal to

  1. fraction numerator 5 over denominator 4 end fraction  
  2. fraction numerator 4 over denominator 5 end fraction  
  3. fraction numerator 7 over denominator 4 end fraction  
  4. fraction numerator 4 over denominator 7 end fraction  

The correct answer is: fraction numerator 5 over denominator 4 end fraction


    r subscript 1 end subscript equals 2 r subscript 2 end subscript equals 3 r subscript 3 end subscript
    rightwards double arrow fraction numerator increment over denominator s minus a end fraction equals 2 fraction numerator increment over denominator s minus b end fraction equals 3 fraction numerator increment over denominator s minus c end fraction
    rightwards double arrow fraction numerator 1 over denominator s minus a end fraction equals fraction numerator 2 over denominator s minus b end fraction equals fraction numerator 3 over denominator s minus c end fraction equals k blank open parentheses s a y close parentheses
    rightwards double arrow s minus a equals fraction numerator 1 over denominator k end fraction comma blank s minus b equals fraction numerator 2 over denominator k end fraction blank a n d blank s minus c equals fraction numerator 3 over denominator k end fraction
    Adding, we getblank 3 s minus open parentheses a plus b plus c close parentheses equals fraction numerator 6 over denominator k end fraction blank rightwards double arrow s equals fraction numerator 6 over denominator k end fraction blank rightwards double arrow a equals fraction numerator 5 over denominator k end fraction blankandblank b equals fraction numerator 4 over denominator k end fraction blank rightwards double arrow fraction numerator a over denominator b end fraction equals fraction numerator 5 over denominator 4 end fraction

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