What is the perimeter of a triangle with corners at #(7 ,3 )#, #(9 ,5 )#, and #(3 ,3 )#?

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Answer 1 · 2018-02-11T17:48:00

#4 + 2sqrt10 + 2sqrt2 ~= 13.15#

Well, perimeter is simply the sum of the sides for any 2D shape.

We have three sides in our triangle: from #(3,3)# to #(7,3)#; from #(3,3)# to #(9,5)#; and from #(7,3)# to #(9,5)#.

The lengths of each are found by Pythagoras' theorem, using the difference between the #x# and the #y# coordinates for a pair of points. .

For the first:

#l_1 = sqrt((7-3)^2+(3-3)^2) = 4#

For the second:

#l_2 = sqrt((9-3)^2+(5-3)^2) = sqrt40 = 2sqrt10~= 6.32#

And for the final one:

#l_3 = sqrt((9-7)^2+(5-3)^2) = sqrt8 = 2sqrt2 ~= 2.83#

so the perimeter is going to be

#P = l_1 + l_2 + l_3 = 4 + 6.32 + 2.83 = 13.15#

or in surd form,

#4 + 2sqrt10 + 2sqrt2#