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      Question

      In a triangle ABC, AB = 13 cm, BC = 14 cm, and AC = 15

      cm. Find the area of the triangle and the length of the altitude from vertex A to side BC.
      A Area = 84 cm², Altitude = 12 cm Correct Answer Incorrect Answer
      B Area = 84 cm², Altitude = 13 cm Correct Answer Incorrect Answer
      C Area = 90 cm², Altitude = 12 cm Correct Answer Incorrect Answer
      D Area = 90 cm², Altitude = 13 cm Correct Answer Incorrect Answer

      Solution

      Using Heron’s formula, s = (AB + BC + AC) / 2 = (13 + 14 + 15) / 2 = 21 cm. Area = √[s(s - AB)(s - BC)(s - AC)] = √[21(21 - 13)(21 - 14)(21 - 15)] = √[21 × 8 × 7 × 6] = √(7056) = 84 cm². Altitude from A = (2 × Area) / BC = (2 × 84) / 14 = 12 cm. Correct Option: a) Area = 84 cm², Altitude = 12 cm

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