# What is the perimeter of a triangle with corners at (3 ,6 ), (1 ,8 ), and (8 ,1 )?

May 4, 2016

Perimeter $= 14 \sqrt{2}$

#### Explanation:

Distance between
$\textcolor{w h i t e}{\text{XXX}} \left(3 , 6\right) \mathmr{and} \left(1 , 8\right) = \sqrt{{\left(3 - 1\right)}^{2} + {\left(6 - 8\right)}^{2}} = \sqrt{{2}^{2} + {2}^{2}} = 2 \sqrt{2}$

$\textcolor{w h i t e}{\text{XXX}} \left(1 , 8\right) \mathmr{and} \left(8 , 1\right) = \sqrt{{\left(1 - 8\right)}^{2} + {\left(8 - 1\right)}^{2}} = \sqrt{{7}^{2} + {7}^{2}} = 7 \sqrt{2}$

$\textcolor{w h i t e}{\text{XXX}} \left(8 , 1\right) \mathmr{and} \left(3 , 6\right) = \sqrt{{\left(8 - 3\right)}^{2} + {\left(1 - 6\right)}^{2}} = \sqrt{{5}^{2} + {5}^{2}} = 5 \sqrt{2}$

Perimeter $= 2 \sqrt{2} + 7 \sqrt{2} + 5 \sqrt{2} = 14 \sqrt{2}$