Question

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

Answer 1

`P=sqrt8 +sqrt18+sqrt50`

`=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 `RR^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((3-5)^2+(9-7)^2)+sqrt((5-8)^2+(7-4)^2)+sqrt((8-3)^2+(4-9)^2)`

`=sqrt8 +sqrt18+sqrt50`

`=14.1421` units.