What is the perimeter of a triangle with corners at #(7 ,2 )#, #(8 ,3 )#, and #(4 ,4 )#?

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Answer 1 · 2017-07-29T20:58:32

#9.14# #"units"#

To find the perimeter of a triangle, add up the lengths of all of its sides. Use the distance formula, #d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#.

Find the distance between #(7,2)# and #(8,3)#:

#d=sqrt((8-7)^2+(3-2)^2) = sqrt(1^2+1^2)=sqrt2#

Find the distance between #(8,3)# and #(4,4)#:

#d=sqrt((4-8)^2+(4-3)^2) = sqrt((-4)^2+1^2)=sqrt17#

Find the distance between #(7,2)# and #(4,4)#:

#d=sqrt((4-7)^2+(4-2)^2) = sqrt((-3)^2+2^2)=sqrt13#

The perimeter is #sqrt2+sqrt17+sqrt13#, or about #9.14# #"units"#.