# Find the perimeter of the triangle whose sides are (1,2) , (3,4) and (-1,5)

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Given the perimeter whose edges are the point A(1,2), B(3,4) and C(-1,5)

We need to find the perimeter of the triangle.

First we need to find the length of the sides

==> We will use the distance between two points formula to calculate the length of the sides.

==> AB = sqrt( 3-1)^2 + (4-2)^2 = sqrt(8) = 2sqrt2

==> BC = sqrt(3+1)^2 + (4-5)^2 = sqrt(17)

==> AC = sqrt(1+1)^2+(2-5)^2 = sqrt(13)

Then the perimeter is:

**P = AB + BC + AC**

** = 2sqrt2 + sqrt17 + sqrt13**

**= 2.83 + 4.12 + 3.61 = 10.56 ( approx.)**

We have to find the perimeter of the triangle with the vertexes (1,2) , (3,4) and (-1,5).

Now we need to find the lengths of the sides of the triangle. These are

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

sqrt [ ( 3 + 1)^2 + ( 4 - 5)^2] = sqrt ( 16 + 1) = sqrt 17.

sqrt [ ( -1 - 1)^2 + ( 5 - 2)^2] = sqrt ( 4 + 9) = sqrt 13

**The perimeter is 2 sqrt 2 + sqrt 17 + sqrt 13.**