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

Question

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

Jayden Jackson · Accepted Answer

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

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..

Claire Akin · Answer

undefined To find the perimeter of a triangle, you need to calculate the sum of the lengths of its three sides. You can use the distance formula to find the lengths of each side, which is the square root of the sum of the squares of the differences in the coordinates of the endpoints.

For the given triangle with corners at (3, 0), (5, 2), and (1, 4), the lengths of the three sides can be calculated as follows:

1. Side 1: From (3, 0) to (5, 2)
   Length = sqrt((5 - 3)^2 + (2 - 0)^2)

2. Side 2: From (5, 2) to (1, 4)
   Length = sqrt((1 - 5)^2 + (4 - 2)^2)

3. Side 3: From (1, 4) to (3, 0)
   Length = sqrt((3 - 1)^2 + (0 - 4)^2)

After calculating the lengths of all three sides, you sum them up to find the perimeter of the triangle.