To find the perimeter of the triangle we need to find the distance between the points:
D and E
E and F
F and D
The formula for calculating the distance between two points is:
#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)#
Distance Between D and E
#d = sqrt((color(red)(-3) - color(blue)(-2))^2 + (color(red)(5) - color(blue)(1))^2)#
#d = sqrt((color(red)(-3) + color(blue)(2))^2 + (color(red)(5) - color(blue)(1))^2)#
#d = sqrt(-1^2 + 4^2)#
#d = sqrt(1 + 16)#
#d = sqrt(17)#
Distance Between E and F
The formula for calculating the distance between two points is:
#d = sqrt((color(red)(3) - color(blue)(-3))^2 + (color(red)(6) - color(blue)(5))^2)#
#d = sqrt((color(red)(3) + color(blue)(3))^2 + (color(red)(6) - color(blue)(5))^2)#
#d = sqrt(6^2 + 1^2)#
#d = sqrt(36 + 1)#
#d = sqrt(37)#
Distance Between F and D
#d = sqrt((color(red)(-2) - color(blue)(3))^2 + (color(red)(1) - color(blue)(6))^2)#
#d = sqrt(-5^2 + (-5)^2)#
#d = sqrt(25 + 25)#
#d = sqrt(25 xx 2)#
#d = sqrt(25)sqrt(2)#
#d = 5sqrt(2)#
Therefore the perimeter of the triangle is:
#sqrt(17) + sqrt(37) + 5sqrt(2)#
If the answer needs to be a number without radicals we have:
#4.123 + 6.083 + (5 xx 1.414) =>#
#4.123 + 6.083 + 7.070 =>#
#17.276# rounded to the nearest thousandth.
