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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 mĀ² Correct Answer Incorrect Answer
    B Height = 50 m, Area = 2,800 mĀ² Correct Answer Incorrect Answer
    C Height = 45 m, Area = 2,520 mĀ² Correct Answer Incorrect Answer
    D Height = 56 m, Area = 3,136 mĀ² Correct Answer Incorrect Answer
    E Height = 36 m, Area = 3,136 mĀ² Correct Answer Incorrect Answer

    Solution

    Use Heronā€™s formula to find the area: s = (50 + 78 + 112)/2 = 120 m. Area = āˆš[s(s - a)(s - b)(s - c)]Ā  = āˆš[120(120 - 50)(120 - 78)(120 - 112)]. = āˆš[120 Ɨ 70 Ɨ 42 Ɨ 8] = āˆš[2822400] = 1680 mĀ². Height corresponding to the longest side = 2 Ɨ Area/BaseĀ  = (2 Ɨ 1680)/112 = 30 m. Correct answer: a) Height = 30 m, Area = 1,680 mĀ²

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