What is the perimeter of a triangle with corners at #(6 ,4 )#, #(9 ,2 )#, and #(5 ,1 )#?

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Answer 1 · 2018-02-10T14:01:19

Perimeter of triangle ABC #= color (green)(10.891)#

Using distance formula, let us calculate the lengths of the triangle.

#d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)#

Given A (6,4), B (9,2), C(5,1)

#vec(AB) = sqrt((9-6)^2 + (2-4)^2) = 3.6056#

#vec(BC) = sqrt((9-5)^2+(2-1)^2) = 4.1231#

#vec(CA) = sqrt((6-5)^2 + (4-1)^2) = 3.1623#

Perimeter of #Delta ABC = vec(AB) + vec(BC) + vec(CA)#

#=> (3.6056 + 4.1231 + 3.1623) = color(green)(10.891)#