# What is the perimeter of a triangle with corners at (1 ,8 ), (8 ,3 ), and (4 ,5 )?

Jun 5, 2016

Perimeter of triangle is $17.317$

#### Explanation:

Perimeter is th sum of all the sides of a polygon including that of a triangle.

Hence let us find the sides of triangle formed by $\left(1 , 8\right)$, $\left(8 , 3\right)$ and $\left(4 , 5\right)$. This will be surely distance between pair of points, which is

$a = \sqrt{{\left(8 - 1\right)}^{2} + {\left(3 - 8\right)}^{2}} = \sqrt{49 + 25} = \sqrt{74} = 8.6023$

$b = \sqrt{{\left(4 - 8\right)}^{2} + {\left(5 - 3\right)}^{2}} = \sqrt{16 + 4} = \sqrt{20} = 4.4721$ and

$c = \sqrt{{\left(1 - 4\right)}^{2} + {\left(8 - 5\right)}^{2}} = \sqrt{9 + 9} = \sqrt{18} = 4.2426$

Hence, perimeter is $8.6023 + 4.4721 + 4.2426 = 17.317$