Question

If BC = 4 and CD = 27, find AC.

Answer 1

$\Delta ABC\sim\Delta DAC\\\\then\\\\\frac{|AC|}{|BC|}=\frac{|CD|}{|AC|}\\\\|AC|^2=|BC|\cdot|CD|\\\\|AC|^2=4\cdot27\\\\|AC|=\sqrt{4\cdot27}\\\\|AC|=\sqrt4\cdot\sqrt{27}\\\\|AC|=2\cdot\sqrt{9\cdot3}\\\\|AC|=2\sqrt9\cdot\sqrt3\\\\|AC|=2\cdot3\sqrt3\\\\|AC|=6\sqrt3$