Area without knowing the side lengths

Geometry Level 3

In a triangle $ABC$ , the medians $AD$ and $BE$ are perpendicular to each other and their lengths are $AD=m$ and $BE=n$ . If the area of triangle $ABC$ is of the form
$\dfrac {amn}b$ , where $a$ and $b$ are coprime positive integers, find $a+b$ .

The answer is 5.

1 solution

Abdullah Ahmed
Sep 12, 2016

As $AD$ and $BE$ are perpendicular to each other, so the area of $ABDE$ is $\frac{1}{2}$ $AD*BE$

So $\frac{3}{4}$ $Area$ = $\frac{1}{2}$ $mn$

$Area$ = $\frac{2}{3}$ $mn$

$a+b$ = $5$

Area without knowing the side lengths

The answer is 5.

1 solution

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