What is the perimeter of a triangle with corners at #(2 ,5 )#, #(9 ,2 )#, and #(3 ,1 )#?

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Answer 1 · 2016-10-12T18:51:59

About #17.82#.

The perimeter is the sum of the lengths of the sides, so, if we call

#A = (2,5)#

#B = (9,2)#

#C = (3,1)#

we have

#2p = AB+BC+AC#, where #2p# is the perimeter.

The formula to find the length of a line, knowing its extreme points' coordinates, is

#PQ = sqrt( (x_P-x_Q)^2 + (y_P-y_Q)^2)#

Applying this formula to all points, we have

#AB = sqrt((-7)^2+3^3)=sqrt(58)=7.62#

#BC = sqrt(6^2+1^2)=sqrt(37)=6.08#

#AC = sqrt( (-1)^2+4^2)=sqrt(17)=4.12#

Thus, #AB+BC+AC=7.62+6.08+4.12=17.82#

Note that all the values of the square roots are approximated!