Answer: The length of AC is 18 ft.
Step-by-step explanation:
By the given diagram,
AM = MB and CN = NB
M and N are the mid points of the sides AB and CB respectively,
Thus, by the mid point theorem,
MN ║ AC,
By the alternative interior angle theorem,
∠BMN ≅ ∠BAC
∠BNM ≅ ∠BCA
Thus, by AA similarity postulate,
ΔBMN ≅ ΔBAC
By the property of similar triangles,
[tex]\frac{BM}{BA}=\frac{MN}{AC}[/tex]
[tex]\frac{BM}{BM+MA}=\frac{MN}{AC}[/tex]
[tex]\frac{4}{4+4}=\frac{9}{AC}[/tex]
[tex]\frac{4}{8}=\frac{9}{AC}[/tex]
[tex]4AC=72\implies AC = 18\text{ ft}[/tex]
Thus, The length of AC is 18 ft.
