It is known that in △ ABC, ab = 20, AC = 15, and the height of BC is 12, then the length of BC is______ ．

Let ad ⊥ BC be D, then ad is the height on the edge of BC, ad = 12. There are two cases: ① high ad is in the triangle, as shown in the figure: in RT △ ADC, ac2 = ad2 + DC2, ｜ DC = 9 is obtained by Pythagorean theorem; in RT △ ADB, AB2 = ad2 + BD2, ｜ BD = 16, ｜ BC = BD + DC = 16 + 9 = 25 is obtained by Pythagorean theorem; ② high ad is outside the triangle, as shown in the figure: in RT △ ADC, ac2 = ad2 + DC2 ｜ is obtained by Pythagorean theorem DC = 9, in RT △ ADB, according to Pythagorean theorem: AB2 = ad2 + BD2, ∧ BD = 16, ∧ BC = bd-dc = 16-9 = 7, so the answer is: 25 or 7

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