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      Question

      A triangle has sides 13 cm, 14 cm, and 15 cm. What is

      the radius of its incircle?
      A 5 cm Correct Answer Incorrect Answer
      B 3 cm Correct Answer Incorrect Answer
      C 2 cm Correct Answer Incorrect Answer
      D 4 cm Correct Answer Incorrect Answer

      Solution

      Sides: a = 13, b = 14, c = 15. Semi-perimeter s = (13 + 14 + 15) / 2 = 42/2 = 21. Area (HeronтАЩs formula): Area = тИЪ[s(s тИТ a)(s тИТ b)(s тИТ c)] = тИЪ[21 ├Ч (21 тИТ 13) ├Ч (21 тИТ 14) ├Ч (21 тИТ 15)] = тИЪ[21 ├Ч 8 ├Ч 7 ├Ч 6] = тИЪ7056 = 84 cm┬▓. Inradius r = Area / s = 84 / 21 = 4 cm.

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