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

Question

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

Mason Adams · Accepted Answer

#P= sqrt(29)+sqrt(18)+sqrt(5)# Use the distance formula using the verteces of a triangle: #A(3,5), B(1,6)# and #C(4,3)# #bar(AB)=sqrt((3-1)^2+(1-6)^2)# following the same strategy for #bar(BC)# and #bar(CA)# #P=sqrt((3-1)^2+(1-6)^2)+sqrt((1-4)^2+(6-3)^2)+sqrt((4-3)^2+(3-5)^2) # #P= sqrt(29)+sqrt(18)+sqrt(5)#

Autumn Armstrong · Answer

undefined To find the perimeter of the triangle with corners at (3, 5), (1, 6), and (4, 3), you need to calculate the distances between these points and then sum them up. You can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by √((x2 - x1)^2 + (y2 - y1)^2).

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

2. Distance between (1, 6) and (4, 3):
   √((4 - 1)^2 + (3 - 6)^2) = √((3)^2 + (-3)^2) = √(9 + 9) = √18 = 3√2

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

Add the distances together to find the perimeter:
Perimeter = √5 + 3√2 + √5 ≈ 2.24 + 4.24 + 2.24 ≈ 8.72

So, the perimeter of the triangle is approximately 8.72 units.