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Answer:
The length of AC is 18 feet ⇒ 4th answer
Step-by-step explanation:
* Lets revise an important theorem for a triangle
- <em>If a line segment joining the mid-points of two sides of a triangle, </em>
<em> then this line segment is parallel to the third side of the triangle and</em>
<em> equal half its length</em>
<em></em>
* Lets use this theorem to solve the problem
- In Δ ABC
∵ Line MN intersects the sides AB at M
∵ MA = MB
∴ M is the mid point of the side AB
∵ Line MN intersects the sides BC at N
∵ NC = NB
∴ N is the mid point of the side BC
- <em>By using the theorem above</em>
In Δ ABC
∵ M is the mid-point of AB
∵ N is the mid-point of BC
∴ MN // AC
∴ MN = AC
∵ The length of MN = 9 feet
∵ MN = AC
∴ 9 = AC
- Multiply both sides by 2
∴ AC = 18 feet
* The length of AC is 18 feet