The perimeter of an object is the length of the outer edge of the object. To solve this problem we need to determine the distance between:
- #(1,5) and #(6, 2)#
- #(6, 2) and #(5, 7)#
- #(5, 7)# and #(1, 5)#
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 #(1,5)# and #(6, 2)#:
#d_1 = sqrt((color(red)(6) - color(blue)(1))^2 + (color(red)(2) - color(blue)(5))^2)#
#d_1 = sqrt(5^2 + (-3)^2)#
#d_1 = sqrt(25 + 9)#
#d_1 = sqrt(34)#
Distance Between #(6, 2)# and #(5, 7)#:
#d_2 = sqrt((color(red)(5) - color(blue)(6))^2 + (color(red)(7) - color(blue)(2))^2)#
#d_2 = sqrt((-1)^2 + 5^2)#
#d_2 = sqrt(1 + 25)#
#d_2 = sqrt(26)#
Distance Between #(5, 7)# and #(1,5)#:
#d_3 = sqrt((color(red)(1) - color(blue)(5))^2 + (color(red)(5) - color(blue)(7))^2)#
#d_3 = sqrt((-4)^2 + (-2)^2)#
#d_3 = sqrt(16 + 4)#
#d_3 = sqrt(20)#
#d_3 = sqrt(4 * 5)#
#d_3 = sqrt(4) * sqrt(5)#
#d_3 = 2sqrt(5)#
The Perimeter of the Triangel is:
#p = d_1 + d_2 + d_3#
#p = sqrt(34) + sqrt(26) + 2sqrt(5)#
If you need the answer as a single number:
#p = 5.831 + 5.099 + (2 xx 2.236)#
#p = 5.831 + 5.099 + 4.472#
#p = 15.402# rounded to the nearest thousandth.
