What is the perimeter of a triangle with vertices located at #(1, 4), (2, 7)#, and #(1, 5)#?

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Answer 1 · 2016-09-07T23:51:24

The perimeter is approximately #6.4# units.

Find each of the lengths using the distance formula and add.

Distance 1: Between #(1,4)# and #(2, 7)#

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

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

#d = sqrt(1 + 9)#

#d = sqrt(10)#

Distance 2: Between #(1,4)# and #(1,5)#

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

#d = sqrt((1 - 1)^2 + (5 - 4)^2)#

#d = sqrt(1)#

#d = 1#

Distance 3: Between #(1,5)# and #(2, 7)#

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

#d = sqrt(1 + 4)#

#d = sqrt(5)#

We now add the distances to find the perimeter.

#P = d_1 + d_2 +d_3#

#P = sqrt(5) + sqrt(10) + 1#

#P ~=6.4#

Hopefully this helps!