$\{AC\}^2 = HC \times BC$ $\{AC\}^2 = 2 \times 10$ $\sqrt{\{AC\}^2} = \sqrt{20} \rightarrow AC = \sqrt{4 \times 5} = 2\sqrt{5}$ $\{AH\}^2 = BH \times CH$ $\{AH\}^2 = 8 \times 2$ $\sqrt{\{AH\}^2} = \sqrt{16} \rightarrow AH = 4$ $\{AB\}^2 = BH \times BC$ $\{AB\}^2 = 8 \times 10$ $\sqrt{\{AB\}^2} = \sqrt{80} \rightarrow AB = \sqrt{16 \times 5} = 4\sqrt{5}$ [شکل: مثلث ABC با ارتفاع AH، مقادیر: AB=z=√5، AC=y=2√5، AH=x، BH=8، HC=2]