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.