# What is the perimeter of a triangle with corners at (2 ,5 ), (9 ,2 ), and (3 ,1 )?

Oct 12, 2016

About $17.82$.

#### Explanation:

The perimeter is the sum of the lengths of the sides, so, if we call

$A = \left(2 , 5\right)$

$B = \left(9 , 2\right)$

$C = \left(3 , 1\right)$

we have

$2 p = A B + B C + A C$, where $2 p$ is the perimeter.

The formula to find the length of a line, knowing its extreme points' coordinates, is

$P Q = \sqrt{{\left({x}_{P} - {x}_{Q}\right)}^{2} + {\left({y}_{P} - {y}_{Q}\right)}^{2}}$

Applying this formula to all points, we have

$A B = \sqrt{{\left(- 7\right)}^{2} + {3}^{3}} = \sqrt{58} = 7.62$

$B C = \sqrt{{6}^{2} + {1}^{2}} = \sqrt{37} = 6.08$

$A C = \sqrt{{\left(- 1\right)}^{2} + {4}^{2}} = \sqrt{17} = 4.12$

Thus, $A B + B C + A C = 7.62 + 6.08 + 4.12 = 17.82$

Note that all the values of the square roots are approximated!