A right triangle has coordinates (-2,2) , (6,8) and (6,2). What is the perimeter of the triangle?

Question

Savannah Anderson · Accepted Answer

The perimeter of the triangle is 24

You must measure the separation between the three point pairs in order to determine the triangle's perimeter. The sequence (-2, 2) and (6, 2) and (6, 2) and (6, 8) The following formula can be used to find the separation between two points: #d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)# After calculating and adding these three distances, we obtain: #p = sqrt((color(red)(6) - color(blue)(-2))^2 + (color(red)(8) - color(blue)(2))^2) + sqrt((color(red)(6) - color(blue)(-2))^2 + (color(red)(2) - color(blue)(2))^2) + sqrt((color(red)(6) - color(blue)(6))^2 + (color(red)(8) - color(blue)(2))^2)# #p = sqrt((color(red)(6) + color(blue)(2))^2 + (color(red)(8) - color(blue)(2))^2) + sqrt((color(red)(6) + color(blue)(2))^2 + (color(red)(2) - color(blue)(2))^2) + sqrt((color(red)(6) - color(blue)(6))^2 + (color(red)(8) - color(blue)(2))^2)# #p = sqrt(8^2 + 6^2) + sqrt(8^2 + 0^2) + sqrt(0^2 + 6^2)# #p = sqrt(64 + 36) + sqrt(64 + 0) + sqrt(0 + 36)# #p = sqrt(100) + sqrt(64) + sqrt(36)# #p = 10 + 8 + 6# #p = 24#

Genesis Allen · Answer

undefined First, we find the lengths of the sides of the triangle using the distance formula. Then, we add these lengths to find the perimeter.

Length of side 1: 
$$
\sqrt{(6 - (-2))^2 + (8 - 2)^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10
$$

Length of side 2:
$$
\sqrt{(6 - 6)^2 + (2 - 8)^2} = \sqrt{0^2 + (-6)^2} = \sqrt{0 + 36} = \sqrt{36} = 6
$$

Length of side 3:
$$
\sqrt{(6 - 6)^2 + (2 - 2)^2} = \sqrt{0^2 + 0^2} = \sqrt{0 + 0} = 0
$$

Now, we add the lengths of the sides:
$$
10 + 6 + 0 = 16
$$

So, the perimeter of the triangle is 16 units.