The AC is 18 feet long.
Triangles are primarily involved in the mid-point theorem. According to this rule, if the midpoints of any two triangle sides are connected, the line formed is parallel to the third side and equal to half of the third side. Contrarily, if a parallel line is drawn from one side's midpoint to any other, it will bisect the third side and be equal to half the side to which it is parallel.
As shown in the diagram,
AM = MB, CN = NB.
The midpoints of the sides AB and CB, respectively, are M and N.
So, according to the midpoint theorem,
MN ║ AC,
The alternative interior angle theorem demonstrates that
∠BMM ≅∠BAC
∠BNM ≅∠BCA
According to the AA similarity postulate,
ΔBMM ≅∠BAC
The characteristic of identical triangles
[tex]\frac{BM}{BA} = \frac{MN}{AC}\\ \frac{BM}{BM+MA} = \frac{MN}{AC}\\ \frac{4}{4+4} = \frac{9}{AC}\\ \frac{4}{8} =\frac{9}{AC} \\[/tex]
4AC=72
AC=18 ft
As a result, AC is 18 feet long.
The complete question is:-
What is the length of the AC?
3 ft
4 ft
9 ft
18 ft
To learn more about the midpoint theorem, refer:-
https://brainly.com/question/28667736
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