Mathematics
Grade9
Easy

Question

If the diagonals of a kite are 1/6x units and (2x+5) units. Express the area in simplified form.

  1. fraction numerator 2 x plus 5 over denominator 3 x end fraction text  units  end text squared
  2. fraction numerator x plus 5 over denominator 6 end fraction text  units  end text squared
  3. fraction numerator 2 x plus 5 over denominator 12 x end fraction text  units  end text squared
  4. fraction numerator 2 x plus 5 over denominator 6 x end fraction text  units  end text squared

The correct answer is: fraction numerator 2 x plus 5 over denominator 12 x end fraction text  units  end text squared


    Write the formula for the area of a kite:
    A equals fraction numerator d subscript 1 times d subscript 2 over denominator 2 end fraction
    Substitute the given diagonals:
    A equals fraction numerator open parentheses fraction numerator 1 over denominator 6 x end fraction close parentheses left parenthesis 2 x plus 5 right parenthesis over denominator 2 end fraction
    Distribute the fraction numerator 1 over denominator 6 x end fraction:
    A equals fraction numerator 1 third plus fraction numerator 5 over denominator 6 x end fraction over denominator 2 end fraction
    Create a common denominator for the two fractions in the numerator:
    A equals fraction numerator fraction numerator 2 x over denominator 6 x end fraction plus fraction numerator 5 over denominator 6 x end fraction over denominator 2 end fraction
A equals fraction numerator fraction numerator 2 x plus 5 over denominator 6 x end fraction over denominator 2 end fraction
    You can consider the outermost division by 2 as multiply everything in the numerator by 1 half.
    A equals open parentheses 1 half close parentheses open parentheses fraction numerator 2 x plus 5 over denominator 6 x end fraction close parentheses
    Multiply across to arrive at the correct answer:
    A equals fraction numerator 2 x plus 5 over denominator 12 x end fraction

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