# What is the perimeter of a triangle with corners at (3 ,5 ), (1 ,6 ), and (4 ,3 )?

Mar 20, 2016

$P = \sqrt{29} + \sqrt{18} + \sqrt{5}$

#### Explanation:

Use the distance formula using the verteces of a triangle:
$A \left(3 , 5\right) , B \left(1 , 6\right)$ and $C \left(4 , 3\right)$
$\overline{A B} = \sqrt{{\left(3 - 1\right)}^{2} + {\left(1 - 6\right)}^{2}}$ following the same strategy for
$\overline{B C}$ and $\overline{C A}$
$P = \sqrt{{\left(3 - 1\right)}^{2} + {\left(1 - 6\right)}^{2}} + \sqrt{{\left(1 - 4\right)}^{2} + {\left(6 - 3\right)}^{2}} + \sqrt{{\left(4 - 3\right)}^{2} + {\left(3 - 5\right)}^{2}}$
$P = \sqrt{29} + \sqrt{18} + \sqrt{5}$