#"to find the perimeter of the triangle we require to"#

#"calculate the lengths of the 3 sides"#

#"perimeter "=AB+AC+BC#

#color(blue)"calculate AB"#

#"Note that the points A and B have the same value of"#

#"x-coordinate which means that AB is a vertical line"#

#"Thus the length of AB is the difference in y-coordinates"#

#rArrAB=6-2=4#

#color(blue)"calculate BC"#

#"Note that the points B and C have the same value of "#

#"y-coordinate which means that BC is a horizontal line"#

#"Thus the length of BC is the difference in x-coordinates"#

#rArrBC=3-(-3)=6#

#color(blue)"calculate AC"#

#"to calculate AC use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(-3,6)" and "(x_2,y_2)=(3,2)#

#AC=sqrt((3+3)^2+(2-6)^2)#

#color(white)(AC)=sqrt(36+16)=sqrt52#

#rArr"perimeter "=4+6+sqrt52~~17.21" to 2 dec. places"#