# Find the perimeter of the polygons with vertices to the given points. 1.(2,3),(5,7),(-3,4)?

Jul 28, 2018

color(blue)("Perimeter of the triangle " = color(green)( sqrt 73 + sqrt 26 + 5 ~~ 18.643

#### Explanation:

Given polygon is a triangle as it has only three vertices.

$\text{Given :} A \left(2 , 3\right) , B \left(5 , 7\right) , C \left(- 3 , 4\right)$

Using distance formula we can find the lengths of the sides

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

$a = \sqrt{{\left(5 - - 3\right)}^{2} + {\left(7 - 4\right)}^{2}} = \sqrt{73}$

$b = \sqrt{{\left(- 3 - 2\right)}^{2} + {\left(4 - 3\right)}^{2}} = \sqrt{26}$

$c = \sqrt{{\left(2 - 5\right)}^{2} + {\left(7 - 3\right)}^{2}} = 5$

color(blue)("Perimeter of the triangle " = p = (a + b + c)

color(green)(p = sqrt 73 + sqrt 26 + 5 ~~ 18.643