What is the perimeter of a triangle with corners at #(1 ,4 )#, #(3 , 2 )#, and #(2 ,7 )#?

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Answer 1 · 2016-07-24T19:48:05

Perimeter #=11.18 units#

Using the distance formula, we can solve for the length of each side of the triangle and then find the sum of those three sides.

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

For the first side we will use the points #(1,4)# and #(3,2)#

#x_1 =1#
#y_1=4#
#x_2=3#
#y_2=2#

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

For the second side we will use the points #(3,2)# and #(2,7)#

#x_1 =3#
#y_1=2#
#x_2=2#
#y_2=7#

#d= sqrt((2-3)^2 + (7-2)^2)#
#d= sqrt((-1)^2 + (5)^2)#
#d= sqrt(1 + 25)#
#d= sqrt(26)#

For the third side we will use the points #(2,7)# and #(1,4)#

#x_1 =2#
#y_1=7#
#x_2=1#
#y_2=4#

#d= sqrt((1-2)^2 + (4-7)^2)#
#d= sqrt((-1)^2 + (-3)^2)#
#d= sqrt(1 + 9)#
#d= sqrt(10)#

#1^(st) side = 2sqrt2# #=2.82#
#2^(nd) side = sqrt26# #=5.10#
#3^(rd) side = sqrt10# #=3.16#

#2sqrt2 + sqrt26 + sqrt10#

#2.82 +5.10+3.16 =#

Perimeter #=11.18 units#