We have the triangle ABC :

A(2,0) B(4,2) C(3,4)

Let us calculate the measure of the sides:

AB = sqrt[(4-2)^2 + (2-0)^2]= sqrt2+4 = sqrt8 = 2sqrt2

BC = sqrt[(3-4)^2 + (4-2)^2]= sqrt(1+4)= sqrt5

AC= sqrt[(3-2)^2 + (4-0)^2]= sqrt(1+16) = sqrt17

Then the perimeter is:

P= AB + AC + BC

= 2sqrt2 + sqrt5 + sqrt17