Question

Type the correct answer in each box. If necessary, round your answer(s) to the nearest hu The vertices of AABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of AABC is ​

Answer 1

22.81

Explanation:

The distance formula can be used to find the distances between pairs of vertices. The perimeter is the sum of those distances.

Side lengths

The distance formula is ...

d = √((x2 -x1)^2 +(y2 -y1)^2)

Using this formula the triangle side lengths are ...

AB = √((6 -(-2))^2 +(2 -2)^2) = √(8^2) = 8

BC = √((0 -6)^2 +(8 -2)^2) = √(6^2 +6^2) = 6√2

CA = √((-2 -0)^2 +(2 -8)^2) = √(4 +36) = √40

The perimeter of the triangle is the sum of these lengths:

P = 8 +6√2 +2√10 ≈ 22.8098

The perimeter is about 22.81 units.