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In a triangle $$ABC$$ right angled at $$A$$, $$AD$$ is the altitude through $$A$$. If $$AD = 2$$ and $$CD = 3$$ then $$AB =$$
In a right triangle, $$AD^2 = BD \cdot CD$$, so $$BD = \frac{4}{3}$$ and $$BC = 3 + \frac{4}{3} = \frac{13}{3}$$. Also $$AB^2 = BD \cdot BC = \frac{4}{3} \times \frac{13}{3} = \frac{52}{9}$$. So $$AB = \frac{\sqrt{52}}{3}$$.
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