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.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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