Perimeter of triangle is calculated by adding up the three sides of the triangle.
In the given triangle ABC, vertices of triangle are given as [tex] A(-2,2) B(0,4) C(1,-2) [/tex]
We calculate the length of side AB by the distance formula which states as :
For the points [tex] (x_{1},y_{1}) and (x_{2},y_{2}) [/tex]
distance =[tex] \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}} [/tex]
AB = [tex] \sqrt{(0+2)^{2} + (4-2)^{2}} = 2\sqrt{2} [/tex]
BC=[tex] \sqrt{(1-0)^{2} + (-2-4)^{2}} = \sqrt{37} [/tex]
AC=[tex] \sqrt{(1+2)^{2} + (-2-2)^{2}} = 5 [/tex]
Perimeter = AB+BC+AC = [tex] =2\sqrt{2} + 5+ \sqrt{37}= 13.911 [/tex]
So, Perimeter = 14 (Rounded to the nearest tenth)
