What is the perimeter of a triangle with corners at #(3 ,0 )#, #(5 ,2 )#, and #(5 ,4 )#?

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Answer 1 · 2016-03-22T00:08:42

#2sqrt(2)+2sqrt(5)+2 ~~ 9.3#

The distance formula tells us that the distance between two points #(x_1, y_1)# and #(x_2, y_2)# is:

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

If #x_1 = x_2# then this simplifies to #abs(y_2-y_1)#

The distance between #(3, 0)# and #(5, 2)# is:

#sqrt((5-3)^2+(2-0)^2) = sqrt(2^2+2^2) = sqrt(8) = 2sqrt(2)#

The distance between #(3, 0)# and #(5, 4)# is:

#sqrt((5-3)^2+(4-0)^2) = sqrt(2^2+4^2) = sqrt(20) = 2sqrt(5)#

This distance between #(5, 2)# and #(5, 4)# is:

#abs(4-2) = 2#

These are the lengths of the three sides, so the perimeter is just the sum:

#2sqrt(2)+2sqrt(5)+2 ~~ 9.3#