Perimeter of median triangle

Geometry Level 2

$ABC$ is a triangle with $AB = 25,$ $BC = 31$ , $CA = 38$ . $D, E$ and $F$ are the midpoints of $BC, CA$ and $AB$ respectively. What is the perimeter of triangle $DEF$ ?

The answer is 47.

1 solution

Arron Kau Staff
May 13, 2014

Since $D, E, F$ are the midpoints, we can see that $DE, EF$ and $FD$ are parallel to, and half the length of, $AB, BC$ and $CA$ respectively. Hence, $DE + EF + FD = \frac{ AB + BC + CA} {2} = \frac{ 25 + 31 + 38} { 2} = \frac{94}{2} = 47$ .

Perimeter of median triangle

The answer is 47.

1 solution

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