Question 1175958
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It's a little more complicated than that. And the answer you show ("1/6") makes no sense....<br>
With the two sets of parallel segments, the figure consists of three similar triangles: ABC, DEC, and GFE.<br>
For triangles ABC and DEC, BC and CE are corresponding parts; given BC=2 and CE=4. the ratio of similarity between those two triangles is 1:2.  That makes DC = 2*AC = 8 and DE = 2*AB = 6.<br>
In triangles DEC and GFE, CE and EF are corresponding parts, so the ratio of similarity between those two triangles is 4:5.  Use that ratio to determine the lengths of side EG and FG.  I leave that much of the problem to you.<br>
Then of course remember that the question that is asked is the sum of the lengths of the sides of all three triangles.<br>
Note the given figure is not at all to scale.  Solving the problem will be easier if you draw a diagram of your own that depicts the figure more accurately.  Start with triangle ABC, for which all side lengths are given; then use the defined parallel segments to complete the drawing.<br>