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      Question

      A triangular field has sides measuring 50 m, 78 m, and

      112 m. Determine the height of the field corresponding to the longest side and also find the area of the field.
      A Height = 30 m, Area = 1,680 m² Correct Answer Incorrect Answer
      B Height = 50 m, Area = 2,800 m² Correct Answer Incorrect Answer
      C Height = 45 m, Area = 2,520 m² Correct Answer Incorrect Answer
      D Height = 56 m, Area = 3,136 m² Correct Answer Incorrect Answer
      E Height = 36 m, Area = 3,136 m² Correct Answer Incorrect Answer

      Solution

      Use Heron’s formula to find the area: s = (50 + 78 + 112)/2 = 120 m. Area = √[s(s - a)(s - b)(s - c)]  = √[120(120 - 50)(120 - 78)(120 - 112)]. = √[120 × 70 × 42 × 8] = √[2822400] = 1680 m². Height corresponding to the longest side = 2 × Area/Base  = (2 × 1680)/112 = 30 m. Correct answer: a) Height = 30 m, Area = 1,680 m²

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