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 lengths 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

The length of AC is 18 feet ⇒ 4th answer

Step-by-step explanation:

* Lets revise an important theorem for a triangle

- If a line segment joining the mid-points of two sides of a triangle,

  then this line segment is parallel to the third side of the triangle and

  equal half its length

* 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

- By using the theorem above

  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