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

Perimeter $P = \sqrt{10} + \sqrt{10} + 2 \sqrt{10} = 4 \sqrt{10} = 12.6491$

#### Explanation:

Let $a$ be the side from (3, 6) to (2, 3)
Let $b$ be the side from (2, 3) to (4, 9)
Let $c$ be the side from (3, 6) to (4, 9)

Use the distance formula

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

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

$b = \sqrt{{\left(2 - 4\right)}^{2} + {\left(3 - 9\right)}^{2}} = \sqrt{40} = 2 \sqrt{10}$

$c = \sqrt{{\left(3 - 4\right)}^{2} + {\left(6 - 9\right)}^{2}} = \sqrt{10}$

God bless....I hope the explanation is useful.