# What is the perimeter of a triangle with corners at (6 ,5 ), (9 ,1 ), and (3 ,4 )?

Jul 3, 2016

It is $12.4$.

#### Explanation:

We need to find the distances between the points.
We start assigning a letter to each point

$A = \left(6 , 5\right) , B = \left(9 , 1\right) , C = \left(3 , 4\right)$

The distances are

$A B = \sqrt{{\left(6 - 9\right)}^{2} + {\left(5 - 1\right)}^{2}} = \sqrt{9 + 16} = 5$

$A C = \sqrt{{\left(6 - 3\right)}^{2} + {\left(5 - 4\right)}^{2}} = \sqrt{9 + 1} \setminus \approx 3.16$

$B C = \sqrt{{\left(9 - 3\right)}^{2} + {\left(1 - 4\right)}^{2}} = \sqrt{9 + 9} \setminus \approx 4.24$.

The perimeter is then

$A B + A C + B C = 5 + 3.16 + 4.24 = 12.4$.