Points B, D, and F are midpoints of the sides of △ACE . EC = 38 and DF = 16. Find AC
If points B, D, and F are the midpoints of the sides of triangle ACE, then we can apply properties of midsegments in a triangle to solve the problem.
The line segment DF is a midsegment which connects the midpoints of two sides of the triangle. In triangle ACE, the midsegment DF will be parallel to side AC and half its length because a midsegment in a triangle is always half the length of the third side (the side it is parallel to).
Since DF is given as 16 units, and it is half the length of side AC, we can calculate the length of AC as follows:
AC = 2 * DF
AC = 2 * 16
AC = 32
Therefore, the length of side AC is 32 units.