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CDS 2023 · PYQ · Geometry · medium

A triangle has sides 13 cm, 14 cm and 15 cm long. What is the length of the smallest altitude of the triangle?

  1. A.11 cm
  2. B.11.2 cm✓ Correct
  3. C.12.2 cm
  4. D.12 cm

Explanation

Area by Heron's: s=21, Area = √(21·8·7·6) = √7056 = 84. Smallest altitude corresponds to longest side (15): h = 2·84/15 = 11.2 cm.
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