Question

What is the perimeter of a triangle with corners at `(1 ,5 )`, `(6 , 2 )`, and `(2 ,7 )`?

Answer 1

Perimeter `P=sqrt(41)+sqrt(5)+sqrt(34)`
Perimeter `P=14.47014411" "`units

Explanation:

let the points be `A(1, 5)`, `B(6, 2)`, `C(2, 7)`

compute lengths of sides a, b , c

`a=sqrt((x_B-x_C)^2+(y_B-y_C)^2)`
`a=sqrt((6-2)^2+(2-7)^2)`
`a=sqrt((4)^2+(-5)^2)`
`a=sqrt(16+25)`
`a=sqrt(41)`

`b=sqrt((x_A-x_C)^2+(y_A-y_C)^2)`
`b=sqrt((1-2)^2+(5-7)^2)`
`b=sqrt((-1)^2+(-2)^2)`
`b=sqrt((1+4)`
`b=sqrt(5)`

`c=sqrt((x_A-x_B)^2+(y_A-y_B)^2)`
`c=sqrt((1-6)^2+(5-2)^2)`
`c=sqrt((-5)^2+(3)^2)`
`c=sqrt(25+9)`
`c=sqrt(34)`

Perimeter `P=sqrt(41)+sqrt(5)+sqrt(34)`
Perimeter `P=14.47014411" "`units