Question 1149590
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(1) Triangles AFE and CFB are similar.  FE=9 and FB=21 are corresponding parts of those triangles, so the ratio of similarity is 9:21 or 3:7.<br>
(2) So let the lengths of corresponding parts AE and CB be 3x and 7x.<br>
(3) ABCG is a parallelogram; BC = 7x and AE = 3x.  Use that to find an expression for the length of EG.<br>
(4) Angles BAG and EGD are congruent because ABCG is a parallelogram.  Angles AEB and GED are congruent because they are vertical angles.<br>
(5) So triangles BAE and DGE are similar.  Sides AE and EG are corresponding parts of those triangles, giving you the ratio of similarity.<br>
(6) BE and ED are also corresponding parts of those triangles.  The length of ED is what you are to find; the length of BE is known from the given information.<br>
(7) Use the ratio of similarity of those two triangles to answer the question.<br>