Question

ae = ec and bf = fc. ba = 18, de = 7, and bc = 14. fe = ?

Explanation:

Step1: Identify mid - segment theorem

Since $AE = EC$ and $BF=FC$, $FE$ is a mid - segment of $\triangle ABC$.

Step2: Apply mid - segment formula

The length of the mid - segment of a triangle is half the length of the third side. The third side here is $AB$. Given $BA = 18$.

Step3: Calculate the length of $FE$

$FE=\frac{1}{2}BA$. Substituting $BA = 18$, we get $FE = 9$.

Answer:

9