# What is the perimeter of a triangle with corners at (1 ,2 ), (8 ,3 ), and (4 ,1 )?

Nov 17, 2016

$P e r i m e t e r \approx 14.7$

#### Explanation:

Given: $A = \left(1 , 2\right) , B = \left(8 , 3\right) \mathmr{and} C = \left(4 , 1\right)$

The length of AB is:

$A B = \sqrt{{\left(8 - 1\right)}^{2} + {\left(3 - 2\right)}^{2}} = \sqrt{50} = 5 \sqrt{2}$

The length of BC is:

$B C = \sqrt{{\left(4 - 8\right)}^{2} + {\left(1 - 3\right)}^{2}} = \sqrt{20} = 2 \sqrt{5}$

The length of CA is:

$C A = \sqrt{{\left(1 - 4\right)}^{2} + {\left(2 - 1\right)}^{2}} = \sqrt{10}$

$P e r i m e t e r = A B + B C + C A$

$P e r i m e t e r = 5 \sqrt{2} + 2 \sqrt{5} + \sqrt{10}$

$P e r i m e t e r \approx 14.7$