Find the perimeter of the triangle whose vetices A(2,3) B(-1, 4) and C (-4,-6)

Given the triangle ABC such
that:

 A(2,3) B(-1,4) c(-4,-6) are the
vertices's.

To find the perimeter, we need to calculate the length
of all 3 sides:

We will use the following distance
formula:

D = sqrt[( xA-xB)^2 + (
yA-yB)^2]

==> AB = sqrt( -1-2)^2+ (
4-3)^2

               = sqrt(9+1) =
sqrt10

==> AB=
sqrt10

AC = sqrt[(-4-2)^2 +
(-6-3)^2

      = sqrt(36+ 81)

       =
sqrt(117)

AC =
sqrt117)

BC= sqrt[(-4+1)^2+ (
-6-4)^2

     = sqrt( 9 + 100)

      =
sqrt(109)

BC =
sqrt(109)

==> The perimeter
is:

 P = AB + AC +
BC

     = sqrt10 + sqrt117 +
sqrt(109)

       = 24. 42 (
approx.)

Then the perimeter is 24.42