+1347 In the diagram below, we have DE = 3EC and AB = DC = 20. Find the length of FG.
+128408 Note that if DE = 3EC
Then 3EC + EC = 20
4EC = 20
EC = 20 / 4 = 5
So DE = 3 * 5 = 15
Note that riangles DFE and BFA are similar
And DE / BA = 15/20 = 3/4
Which also means that DF / BF = 3/4
So BF / BD = BF / (BF + FD) = 4 / (4 + 3) = 4/7
And triangle FGB is similar to triangle DCB
So
FG / DC = BF / BD
FG / 20 = (4/7)
FG = 20 (4/7) = 80/7
