Question

What is the length of Line segment AC?A) 3 ftB) 4 ftC) 18 ftD) 12 ft

Answer 1

A line which bisects two sides of a triangle is parallel to the third.

`MN\parallel AC`

From this fact, we can conclude that the triangles ΔMBN and ΔABC are similar. Since those triangles are similar, the ratio between their corresponding sides are equal.

`(AB)/(MB)=(AC)/(MN)`

Since the point M bisects the side AB, AB is twice the size of MB.

`AB=2MB`

Using this statement in our previous expression, we have

`(2MB)/(MB)=(AC)/(MN)\Rightarrow2=(AC)/(MN)\Rightarrow AC=2MN`

Since the value of MN is given, to find AC we just need to substitute its value on the previous equation

`AC=2\cdot6=12`

The length of AC is 12 ft.