# What is the perimeter of a triangle with corners at (2 ,6 ), (4 ,2 ), and (3 ,1 )?

Oct 2, 2017

Perimeter $= 10.985$

#### Explanation:

Let A(2,6), B(4,2) & C(3,1) be the vertices and their coordinates.
$A B = \sqrt{{\left(4 - 2\right)}^{2} + {\left(2 - 6\right)}^{2}} = \sqrt{{2}^{2} + {4}^{2}} = 2 \sqrt{5}$
$B C = \sqrt{{\left(3 - 4\right)}^{2} + {\left(1 - 2\right)}^{2}} = \sqrt{2}$
$C A = \sqrt{{\left(2 - 3\right)}^{2} + {\left(6 - 1\right)}^{2}} = \sqrt{1 + 25} = \sqrt{26}$
Perimeter $= A B + B C + C A = 2 \sqrt{5} + \sqrt{2} + \sqrt{26}$
Perimeter$= 4.472 + 1.414 + 5.099 = 10.985$