What is the perimeter of a triangle with corners at (6 ,5 ), (8 ,2 ), and (4 ,7 )?

1 Answer
Loweena Gonasegaran
Mar 3, 2018

Perimeter = 62

Explanation:

Let (6,5) = A , (8,2) = B and (4,7) = C
Formula of distance between points is :
sqrt ((x_2-x_1)^2+(y_2-y_1)^2
Find the distance between A and B:
Let (6,5) = (x_1,y_1) and (8,2) = (x_2,y_2)
=> sqrt ((8-6)^2+(2-5)^2)
=> sqrt ((2)^2+(-3)^2)
=> sqrt ((4+9)^2)
=> sqrt ((13)^2)
=> 13

Find the distance between B and C:
Let (8,2) = (x_1,y_1) and (4,7) = (x_2,y_2)
=> sqrt ((4-8)^2+(7-2)^2)
=> sqrt ((-4)^2+(5)^2)
=> sqrt ((16+25)^2)
=> sqrt ((41)^2)
=> 41

Find the distance between C and A:
Let (4,7) = (x_1,y_1) and (6,5) = (x_2,y_2)
=> sqrt ((6-4)^2+(5-7)^2)
=> sqrt ((2)^2+(-2)^2)
=> sqrt ((4+4)^2)
=> sqrt ((8)^2)
=> 8

Perimeter = AB + BC + CA
=> 13 + 41 + 8
=> 62

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