# What is the perimeter of a triangle with corners at (6 ,4 ), (8 ,2 ), and (4 ,7 )?

Oct 28, 2016

Perimeter: $\textcolor{g r e e n}{12.8371}$ (approx.)

#### Explanation:

Using the Pythagorean Theorem, find the length of the side between each pair of corners:
$\left\mid \left(6 , 4\right) : \left(8 , 2\right) \right\mid$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{\left(8 - 6\right)}^{2} + {\left(2 - 4\right)}^{2}} = 2 \sqrt{2}$

$\left\mid \left(8 , 2\right) : \left(4 , 7\right) \right\mid$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{\left(4 - 8\right)}^{2} + {\left(2 - 7\right)}^{2}} = \sqrt{41}$

$\left\mid \left(4 , 7\right) : \left(6 , 4\right) \right\mid$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{\left(6 - 4\right)}^{2} + {\left(4 - 7\right)}^{2}} = \sqrt{13}$

The perimeter is the sum of the sides.

Perimeter $= 2 \sqrt{2} + \sqrt{41} + \sqrt{13}$
$\textcolor{w h i t e}{\text{XXX}} \approx 12.8371$ (using a calculator)