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Point O is the centroid of triangle ABC. If FO = 2x -8 and FB = 3x + 3, find x

Point O Is The Centroid Of Triangle ABC If FO 2x 8 And FB 3x 3 Find X class=

Sagot :

The centroid of a triangle is the geometric center of the triangle. It is the intersection point of the 3 medians in a triangle.

The centroid divides each median in a ratio of 2:1.

The median FB is divided into FO and OB in the ratio 1:2.

We can write >>>

[tex]\frac{FO}{FB}=\frac{1}{3}[/tex]

Substituting the information we know, we can find "x". The steps are shown below >>>

[tex]\begin{gathered} \frac{FO}{FB}=\frac{1}{3} \\ \frac{2x-8}{3x+3}=\frac{1}{3} \\ 3(2x-8)=1(3x+3) \\ 6x-24=3x+3 \\ 6x-3x=3+24 \\ 3x=27 \\ x=\frac{27}{3} \\ x=9 \end{gathered}[/tex]Answer[tex]x=9[/tex]

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