midpoints of triangles

Quote:

Originally Posted by Pai-Pai

so the problem says use triangle ghj, where a,b,c are the midpoints. if ab= 3x +8 and gj= 2x + 24, what is ab? i have no idea what that says it's like talking latin. help!!!!!!!!!!! :confused:

You have to use the "mid parallel theorem" (I don't know if this is the appropriate expression in English): "The connection of the midpoints of two sides of a triangle is parallel to the third side and has half of the length of the third side"

I've attached a sketch.

From your question you know that

$2 \cdot |\overline{AB}| = |\overline{GJ}|$

$2(3x+8) = 2x+24 ~\implies~x = 2$

Therefore $|\overline{AB}| = 14$