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Find the pero bisector of mn find the value of x and the perimeter of MNG

Find the pero bisector of mn find the value of x and the perimeter of MNG-example-1
User Masato Nakazawa
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1 Answer

21 votes
21 votes

Since HG is the perpendicular bisector of MN, NH=HM; thus, HM=8. Furthermore,


\begin{gathered} \angle NHG=90degree \\ \text{and} \\ \angle MHG=90degree \end{gathered}

Thus, NHG and MHG are right triangles that have two sides of equal length


\begin{gathered} HG=HG \\ \text{and} \\ NH=HM \end{gathered}

Therefore,


\Rightarrow\Delta\text{HGN}\cong\Delta HGM

Finally,


\begin{gathered} \Rightarrow GN=GM \\ \Rightarrow2x=21-x \\ \Rightarrow3x=21 \\ \Rightarrow x=7 \end{gathered}

And the perimeter of triangle MNG is


\begin{gathered} P=NG+NM+MG=NG+(NH+HM)+MG=2x+(8+8)+21-x \\ \Rightarrow P=x+37 \\ \Rightarrow P=7+37=44 \end{gathered}

Therefore, the answers are x=7, and the Perimeter of MNG is equal to 44

User Lynxlynxlynx
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