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

Q: Answer-A triangular field has sides measuring 50 m, 78 m, and 112 m. Determine the height of the field corr...

Use Herons formula to find the area s 50 78 1122 120 m. Area ss - as - bs - c 120120 - 50120 - 78120 - 112. 120 70 42 8 2822400 1680 m. Height corresponding to the longest side 2 AreaBase 2 1680112 30 m. Correct answer a Height 30 m, Area 1,680 m

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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