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If the three sides of a triangle are 15cm, 20cm and 25cm in length, what is the height of the longest side of the triangle______ cm．
As shown in the figure: let AB = 25 be the longest edge, AC = 15, BC = 20, pass C to make CD ⊥ AB in D, ∵ ac2 + BC2 = 152 + 202 = 625, AB2 = 252 = 625, ∵ ac2 + BC2 = AB2, ∵ C = 90 °, ∵ s △ ACB = 12ac × BC = 12ab × CD, ∵ AC × BC = ab × CD15 × 20 = 25CD, ∵ CD = 12 (CM); so the answer is: 12
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