9th Class Mathematics Heron's Formula Question Bank Herons Formula

  • question_answer
    Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of ` 7 per \[{{m}^{2}}.\]

    A)  ` 9500                        

    B)         ` 11000                       

    C)         ` 10500                       

    D)         ` 12500

    Correct Answer: C

    Solution :

    Let sides of triangular field be a = 50 m, b = 65 m and c = 65 m Semi-perimeter of triangular field.\[s=\frac{a+b+c}{2}\] \[=\left( \frac{50+65+65}{2} \right)m=\frac{180}{2}m=90\,m\] Area of triangular field \[=\sqrt{90(90-50)(90-65)(90-65)}\,{{m}^{2}}\] \[=\sqrt{90\times 40\times 25}\,{{m}^{2}}=1500\,{{m}^{2}}\] \[\because \]Cost of laying grass in \[1\,{{m}^{2}}\]area = ` 7 \[\therefore \]Cost of laying grass in \[1500\,{{m}^{2}}\]area = ` \[(7\times 1500)=\]` 10500


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