What is the perimeter of a triangle with corners at (1 ,5 ), (6 , 2 ), and (2 ,7 )?

1 Answer

Perimeter P=sqrt(41)+sqrt(5)+sqrt(34)
Perimeter P=14.47014411" "units

Explanation:

let the points be A(1, 5), B(6, 2), C(2, 7)

compute lengths of sides a, b , c

a=sqrt((x_B-x_C)^2+(y_B-y_C)^2)
a=sqrt((6-2)^2+(2-7)^2)
a=sqrt((4)^2+(-5)^2)
a=sqrt(16+25)
a=sqrt(41)

b=sqrt((x_A-x_C)^2+(y_A-y_C)^2)
b=sqrt((1-2)^2+(5-7)^2)
b=sqrt((-1)^2+(-2)^2)
b=sqrt((1+4)
b=sqrt(5)

c=sqrt((x_A-x_B)^2+(y_A-y_B)^2)
c=sqrt((1-6)^2+(5-2)^2)
c=sqrt((-5)^2+(3)^2)
c=sqrt(25+9)
c=sqrt(34)

Perimeter P=sqrt(41)+sqrt(5)+sqrt(34)
Perimeter P=14.47014411" "units