# Calculate the perimeter of the triangle with the vertices A (2; 3) B (1; 4) C (-4; 2).

The perimeter of the triangle ABC is calculated by the formula:

P = AB + BC + AC.

It is necessary to find the lengths of the sides of the triangle, for this we first find the coordinates of the vectors AB, BC and AC:

AB (1 – 2; 4 – 3), AB (-1; 1)
BC (- 4 – 1; 2 – 4); BC (-5; -2)
AC (- 4 – 2; 2 – 3) AC (-6; -1)
The length of a vector by its coordinates is calculated by the formula:

L ^ 2 = x ^ 2 + y ^ 2.

Let’s find the lengths of the sides of the triangle:

AB ^ 2 = 1 + 1 = 2; AB = √2
BC ^ 2 = 25 + 4 = 29; BC = √29
AC ^ 2 = 36 + 1 = 37; AC = √37
We get the perimeter of the triangle:

P = √2 + √29 + √37, which is approximately equal to 12.9 units.

Answer: √2 + √29 + √37 or 12.9 units.

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