Question

What is the perimeter of a triangle with corners at `(6 ,4 )`, `(8 ,2 )`, and `(4 ,7 )`?

Answer 1

Perimeter: `color(green)(12.8371)` (approx.)

Explanation:

Using the Pythagorean Theorem, find the length of the side between each pair of corners:
`abs((6,4):(8,2))`
`color(white)("XXX")=sqrt((8-6)^2+(2-4)^2)=2sqrt(2)`

`abs((8,2):(4,7))`
`color(white)("XXX")=sqrt((4-8)^2+(2-7)^2)=sqrt(41)`

`abs((4,7):(6,4))`
`color(white)("XXX")=sqrt((6-4)^2+(4-7)^2)=sqrt(13)`

The perimeter is the sum of the sides.

Perimeter `= 2sqrt(2)+sqrt(41)+sqrt(13)`
`color(white)("XXX")~~12.8371` (using a calculator)