The medians `A D\ a n d\ B E` of a triangle with vertices `A(0, b),\ B(0,0)\ a n d\ C(a ,0)` are perpendicular to each other, if `a=b/2` b. `b=a/2` c. `a b=1` d. `a=+-sqrt(2)b`

Explanation

A median in a triangle is a line passing thought a vertex and through the midpoint of the side opposite to the vertex.


`{D} `is the midpoint of side `{BC}`



`{D}=(\frac{{a}}{2}, 0)`


slope of `AD=\frac{{b}-0}{0-{a} / 2}=\frac{-2 {~b}}{{a}}`

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