Question

the hypotenuse of a right triangle has endpoints (2,7) and (11,-5) what is the perumeter of the triangle?

Answer 1

36 units

Explanation:

Using the coordinates, you can find the length of each leg of the triangle.

Find the distance between the x-coordinates, 2 and 11 by subtracting.

11 - 2 = 9.

Find the distance between the y-coordinates, 7 and -5 by subtracting.

7 - (-5)

7 + 5 = 12

The two legs of the right triangle are 9 and 12.

Use the pythagorean theorom to find the hypotenuse.

`a^(2) +b^(2) =c^(2) \\9^(2) +12x^(2) =c^(2) \\81 + 144 = c^(2) \\225 = c^(2) \\√(225)=\sqrt{c^(2) } \\c = 15`

The three sides of the triangle are 9, 12, and 15. To find the perimeter, add the sides together.

9 + 12 + 15 = 36