Area without knowing the side lengths

Geometry Level 3

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


The answer is 5.

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1 solution

Abdullah Ahmed
Sep 12, 2016

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

So 3 4 \frac{3}{4} A r e a Area = 1 2 \frac{1}{2} m n mn

A r e a Area = 2 3 \frac{2}{3} m n mn

a + b a+b = 5 5

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