A line which bisects two sides of a triangle is parallel to the third.
[tex]MN\parallel AC[/tex]
From this fact, we can conclude that the triangles ΔMBN and ΔABC are similar. Since those triangles are similar, the ratio between their corresponding sides are equal.
[tex]\frac{AB}{MB}=\frac{AC}{MN}[/tex]
Since the point M bisects the side AB, AB is twice the size of MB.
[tex]AB=2MB[/tex]
Using this statement in our previous expression, we have
[tex]\frac{2MB}{MB}=\frac{AC}{MN}\Rightarrow2=\frac{AC}{MN}\Rightarrow AC=2MN[/tex]
Since the value of MN is given, to find AC we just need to substitute its value on the previous equation
[tex]AC=2\cdot6=12[/tex]
The length of AC is 12 ft.
