Question

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

Answer 1

The perimeter of the triangle is 24

Explanation:

To find the perimeter of the triangle you need to find the distance between the three pairs of point.

(-2, 2) and (6, 8)
(-2, 2) and (6, 2)
(6, 2) and (6, 8)

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)`

Calculating these three distances and then adding gives:

`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`