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

1 Answer

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..