Question

What is the perimeter of a triangle with corners at `(3 ,0 )`, `(5 ,2 )`, and `(1 ,4 )`?

Answer 1

Perimeter `P=2sqrt2+4sqrt5=11.772699`

Explanation:

Compute perimeter

Let `A(x_a, y_a)=A(3,0)`
Let `B(x_b, y_b)=B(5, 2)`
Let `C(x_c, y_c)=C(1, 4)`

Perimeter `P=d_a+d_b+d_c`
#P=sqrt((x_b-x_c)^2+(y_b-y_c)^2)+sqrt((x_a-x_c)^2+(y_a-y_c)^2)+ sqrt((x_b-x_a)^2+(y_b-y_a)^2)#

`P=sqrt((5-1)^2+(2-4)^2)+sqrt((3-1)^2+(0-4)^2)+sqrt((5-3)^2+(2-0)^2)`

`P=sqrt((4)^2+(-2)^2)+sqrt((2)^2+(-4)^2)+sqrt(2^2+2^2)`
`P=sqrt20+sqrt20+sqrt8`
`P=2sqrt2+4sqrt5`
`P=11.772699`

God bless...I hope the explanation is useful..