A triangle has sides 13 cm, 14 cm and 15 cm long. What is the length of the <strong>SMALLEST</strong> altitude of the triangle?

Explanation

Area of the triangle using Heron's formula (s=21): \sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \times 8 \times 7 \times 6} = 84 sq cm. The smallest altitude corresponds to the longest base (15 cm). \frac{1}{2} \times 15 \times h = 84 \implies h = \frac{168}{15} = 11.2 cm.

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