# What is the perimeter of a triangle with corners at (9 ,2 ), (6 ,3 ), and (4 ,7 )?

Jun 22, 2016

Perimeter is $14.7055$

#### Explanation:

For finding perimeter of the triangle, we will have to first find all the sides of the triangle, which can be done use distance formula between every set of two points.

Hence, let us find the sides of triangle formed by $\left(9 , 2\right)$, $\left(6 , 3\right)$ and $\left(4 , 7\right)$ by using distance formula $\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

The distance between pair of points will be

$a = \sqrt{{\left(6 - 9\right)}^{2} + {\left(3 - 2\right)}^{2}} = \sqrt{9 + 1} = \sqrt{10} = 3.1623$

$b = \sqrt{{\left(4 - 6\right)}^{2} + {\left(7 - 3\right)}^{2}} = \sqrt{4 + 16} = \sqrt{20} = 4.4721$ and

$c = \sqrt{{\left(4 - 9\right)}^{2} + {\left(7 - 2\right)}^{2}} = \sqrt{25 + 25} = \sqrt{50} = 7.0711$

Hence,, Perimeter is $3.1623 + 4.4721 + 7.0711 = 14.7055$