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The figure shows triangle A E C with segments F B and B D and D F connecting the three sides of the triangle. Point F is on side E A. point B is on side A C. point D is on side C E.
Points B, D, and F are midpoints of the sides of △ACE
. EC = 38 and DF = 16. Find AC. The diagram is not to scale.
Since B, D, and F are midpoints, we know that BD = DF and BF = FC.
Therefore, we can conclude that DC = 2DF = 2(16) = 32.
Since EC = 38 and DC = 32, we can find AC by subtracting DC from EC:
AC = EC - DC = 38 - 32 = 6.
Therefore, AC = 6.