What is the perimeter of a triangle with corners at #(3 ,7 )#, #(1 ,3 )#, and #(4 ,9 )#?

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Answer 1 · 2017-05-18T07:36:51

#= 6 sqrt5# unit

Let say #A(3,7), B(1,3) and C(4,9)#
The distance #D#, between 2 point #(x_1,y_1) and (x_2, y_2)# is given by

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

therefore,
the distance between A& B #= sqrt((3-1)^2 +( 7-3)^2) = sqrt 20#

the distance between B&C #= sqrt((1-4)^2 +( 3-9)^2) = sqrt 45#

the distance between C&A #= sqrt((4-3)^2 +( 9-7)^2) = sqrt 5#

Total perimenter,
#= sqrt20 + sqrt 45 + sqrt 5#

#= sqrt(4*5) + sqrt(9*5) + sqrt5#

#= 2 sqrt(5) + 3sqrt(5) + sqrt5#
#= 6 sqrt5# unit