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alina1380 [7]
3 years ago
11

Triangle A B C is cut by line segment M N. Line segment M N goes from side A B to side B C. The length of M N is 9 feet. The len

gths of B M and M A are 4 feet. The lengths of B N and N C are 3 feet. What is the length of Line segment A C? 3 ft 4 ft 9 ft 18 ft
Mathematics
2 answers:
katrin [286]3 years ago
7 0

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 = \frac{1}{2} AC

∵ The length of MN = 9 feet

∵ MN = \frac{1}{2} AC

∴ 9 = \frac{1}{2} AC

- Multiply both sides by 2

∴ AC = 18 feet

* The length of AC is 18 feet

Sliva [168]3 years ago
5 0

Answer:

The length of AC is 18 feet ⇒ 4th answer

Step-by-step explanation:

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