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

1 Answer
Jan 5, 2018

See a solution process below:

Explanation:

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.