Question

A triangle has vertices (-1, 2), (3, 1), and (7, 2). What is the approximate perimeter of the triangle? Round your answer to the nearest hundredth.

Answer 1

Explanation:

Answer 2

Use the distance formula to find the length of the sides, then add them up to find the perimeter.


`\sf d=√((x_2-x_1)^2+(y_2-y_1)^2)`

For points in the form of (x1, y1), (x2, y2).

(-1, 2), (3, 1)


`\sf d=√((3+1)^2+(1-2)^2)`


`\sf d=√((4)^2+(-1)^2)`


`\sf d=√(16+1)`


`\sf d=√(17)`

(3, 1), (7, 2)


`\sf d=√((7-3)^2+(2-1)^2)`


`\sf d=√((4)^2+(1)^2)`


`\sf d=√(16+1)`


`\sf d=√(17)`

(7, 2), (-1, 2)


`\sf d=√((-1-7)^2+(2-2)^2)`


`\sf d=√((-8)^2+(0)^2)`


`\sf d=√(64+0)`


`\sf d=√(64)=8`

So the perimeter will be:


`\sf 8+√(17)+√(17)\approx\boxed{\sf 16.25}`