The medians $AD$ and $BE$ of a triangle $ABC$ with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are perpend

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The medians $AD$ and $BE$ of a triangle $ABC$ with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are perpendicular to each other if :

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Sol. [Key Concept: Medians $AD \perp BE$ ⇒ slope product $- 1$ gives the relation between $a$ and $b$.]$$AD\bot BE $$$$\begin{matrix} & \ \Rightarrow \ \left( \frac{b}{a} ight)\frac{- b}{(a/2)} = - 1 \ & \ \Rightarrow \ 2b^{2} = a^{2} \ & \ \Rightarrow \ a = \pm \sqrt{2}b \end{matrix}$$

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