Points B, D, and F are midpoints of the sides of the triangle ACE. EC =39 and DF = 16. Find AC.
AC = 2(EC) + DF = 2(39) + 16 = 94
i need to show the work
Since B, D, and F are midpoints of the sides of triangle ACE, we can use the midsegment theorem to find the length of AC.
According to the midsegment theorem, the length of the midsegment in a triangle is equal to half the length of the parallel side.
In this case, the midsegment DF is parallel to the side AC. Therefore, DF is half the length of AC.
We are given that DF = 16, so AC = 2 * DF = 2 * 16 = 32.
Therefore, AC = 32.
To find AC, we need to use the fact that points B, D, and F are midpoints of the sides of triangle ACE. This means that BD and DF are equal to half the lengths of AE and EC, respectively.
Given that DF = 16, we can conclude that EC is also 16 since BD = DF.
Now, since EC = 39, we can find AE by doubling EC: AE = 2 * EC = 2 * 16 = 32.
To find AC, we add AE and EC: AC = AE + EC = 32 + 39 = 71.
Therefore, AC is equal to 71.