[tex] d(B,AC) = BE\\ \\ S_{\triangle ABC}= \frac{AD\cdot BC}{2} = \frac{BE\cdot AC}{2} \Rightarrow AD\cdot BC = BE\cdot AC \Rightarrow \\ \\ \Rightarrow 10\cdot 18=BE\cdot 15\Rightarrow \\ \\ \Rightarrow BE = \frac{10\cdot 18}{15} \Rightarrow BE = \frac{2\cdot 18}{3} \Rightarrow BE = 2\cdot 6 \Rightarrow BE = 12 [/tex]
