Question

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

Answer 1

18 ft

Explanation:

Edg 2020

Answer 2

The length of AC is 18 feet ⇒ 4th answer

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 =
`(1)/(2)` AC

∵ The length of MN = 9 feet

∵ MN =
`(1)/(2)` AC

∴ 9 =
`(1)/(2)` AC

- Multiply both sides by 2

∴ AC = 18 feet

* The length of AC is 18 feet