Question

1. points b, d, and f are mid - points of the sides of △ace. ec = 44 and df = 15. find ac.

Explanation:

Step1: Recall mid - point theorem

In a triangle, the line segment joining the mid - points of two sides is parallel to the third side and half its length. Since F and D are mid - points of AE and EC respectively, in $\triangle AEC$, $FD\parallel AC$ and $FD=\frac{1}{2}AC$.

Step2: Solve for AC

Given $FD = 15$, from the formula $FD=\frac{1}{2}AC$, we can find AC by multiplying both sides of the equation by 2. So, $AC = 2\times FD$.

Answer:

30