What is the perimeter of a triangle with corners at (3 ,9 ), (5 ,7 ), and (8 ,4 )?

Mar 28, 2016

$P = \sqrt{8} + \sqrt{18} + \sqrt{50}$

$= 14.1421$ units.

Explanation:

Perimeter is distance right around the exterior of the closed figure so we find the distances between each point using the normal Euclidean metric in ${\mathbb{R}}^{2}$ and then adding all the distances up.

therefore P=d[(3,9);(5,7)]+d[(5,7);(8,4)]+d[(8,4);(3,9)]

$= \sqrt{{\left(3 - 5\right)}^{2} + {\left(9 - 7\right)}^{2}} + \sqrt{{\left(5 - 8\right)}^{2} + {\left(7 - 4\right)}^{2}} + \sqrt{{\left(8 - 3\right)}^{2} + {\left(4 - 9\right)}^{2}}$

$= \sqrt{8} + \sqrt{18} + \sqrt{50}$

$= 14.1421$ units.