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

What Is The Length Of Line Segment ACA 3 FtB 4 FtC 18 FtD 12 Ft class=

Sagot :

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

[tex]MN\parallel AC[/tex]

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.

[tex]\frac{AB}{MB}=\frac{AC}{MN}[/tex]

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

[tex]AB=2MB[/tex]

Using this statement in our previous expression, we have

[tex]\frac{2MB}{MB}=\frac{AC}{MN}\Rightarrow2=\frac{AC}{MN}\Rightarrow AC=2MN[/tex]

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

[tex]AC=2\cdot6=12[/tex]

The length of AC is 12 ft.

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