What is the perimeter of a triangle with corners at #(2 ,5 )#, #(9 ,2 )#, and #(3 ,8 )#?

1 Answer
Jarob R G.
Apr 12, 2018

#sqrt(58) + sqrt(72) + sqrt(10)#

Explanation:

This requires you to apply the distance formula three times. Recall that the distance between two points #(x_1, y_1)# and #(x_2, y_2)# is #D = sqrt( (x_2 - x_1)^2 + (y_2 - y_1)^2 )#.

The distance between #(2, 5)# and #(9, 2)# is #D_1 = sqrt( (9 - 2)^2 + (2 - 5)^2 ) = sqrt( 49 + 9) = sqrt(58)#.

The distance between #(9, 2)# and #(3, 8)# is #D_2 = sqrt( (3-9)^2 + (8-2)^2 ) = sqrt(36 + 36) = sqrt(72)#.

The distance between #(3, 8)# and #(2, 5)# is #D_3 = sqrt( (2 - 3)^2 + (5 - 8)^2 ) = sqrt(1 + 9) = sqrt(10)#.

The perimeter is thus #P = D_1 + D_2 + D_3 = sqrt(58) + sqrt(72) + sqrt(10)#.

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