Perimeter is ##23.558##

To find the perimeter of a triangle with vertices of ##(1,2)##, ##(3,−4)## and ##(−4,5)##, we have to first find distance between each pair of points, which will give length of sides. For this we use distance formula between two points ##(x_1,y_1)## and ##(x_2,y_2)## is ##sqrt((x_2-x_1)^2+(y_2-y_1)^2)##. Hence if lengths of sides are ##L_1,L_2,L_3##, these are as follows:

##L_1=sqrt((3-1)^2+((-4)-(2))^2)=sqrt(2^2+(-6)^2)=sqrt(4+36)=sqrt40=2sqrt10=6.325##

##L_2=sqrt((-4-(3))^2+(5-(-4))^2)=sqrt((-7)^2+9^2)=sqrt(49+81)=sqrt130=11.402##

##L_3=sqrt((-4-1)^2+(5-2)^2)=sqrt((-5)^2+3^2)=sqrt(25+9)=sqrt34=5.831##

Hence Perimeter is ##6.325+11.402+5.831=23.558##