What is the perimeter of a triangle with corners at #(7 ,6 )#, #(4 ,5 )#, and #(3 ,1 )#?

Question

What is the perimeter of a triangle with corners at #(7 ,6  )#, #(4 ,5  )#, and #(3 ,1  )#?

Autumn Armstrong · Accepted Answer

#Perimeter=sqrt10+sqrt17+sqrt41# Equation for finding distance between #2# coordinates #=# #sqrt((x_2-x_1)^2+(y_2-y_1)^2)# Let, #(7,6)=#point #A# #(4,5)=#point #B# #(3,1)=#point #C# Distance between #AB# #x_1=7,x_2=4,y_1=6,y_2=5# #AB=sqrt((4-7)^2+(5-6)^2)# #=>sqrt((-3)^2+(-1)^2# #=>sqrt(9+1)# #=>sqrt10# #AB=sqrt10# Distance between #BC# #x_1=4,x_2=3,y_1=5,y_2=1# #BC=sqrt((3-4)^2+(1-5)^2)# #=>sqrt((-1)^2+(-4)^2# #=>sqrt(1+16)# #sqrt17# #BC=sqrt17# Distance between #AC# #x_1=7,x_2=3,y_1=6,y_2=1# #AC=sqrt((3-7)^2+(1-6)^2)# #=>sqrt((-4)^2+(-5)^2# #=>sqrt(16+25)# #=>sqrt41# #AC=sqrt41# Perimeter of a triangle is the sum of its #3# sides, that #AB+BC+AC.# #Perimeter=sqrt10+sqrt17+sqrt41#

Avery Allen · Answer

undefined To find the perimeter of a triangle with corners at (7, 6), (4, 5), and (3, 1), you calculate the distance between each pair of points and then sum those distances together.

Using the distance formula √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of two points:

Distance between (7, 6) and (4, 5):
√((4 - 7)^2 + (5 - 6)^2) = √((-3)^2 + (-1)^2) = √(9 + 1) = √10

Distance between (4, 5) and (3, 1):
√((3 - 4)^2 + (1 - 5)^2) = √((-1)^2 + (-4)^2) = √(1 + 16) = √17

Distance between (3, 1) and (7, 6):
√((7 - 3)^2 + (6 - 1)^2) = √((4)^2 + (5)^2) = √(16 + 25) = √41

Perimeter = √10 + √17 + √41