Answer:
B, 19.1
Step-by-step explanation:
Imagine that each side is the hypotenuse of a triangle. You want to use the Pythagorean theorem on each of these triangles to find the length of the side.
Let's start with AB:
One side of the triangle is the distance between the points in the x direction only. A is at the x-coordinate of -3 while B is at the x-coordinate of 2. The side is, thus, 5 units.
The other side of the triangle is the distance between the points in the y direction only. A is at the y-coordinate of 5, while B is at 6. The distance is 1 unit.
So we have a triangle with the base of 5 and the height of 1. The Pythagorean theorem says:
Base² + Height² = Hypotenuse²
Or
a² + b² = c²
where a, b are the sides, and c is the hypotenuse.
Put our values into this, the base is 5 and the height is 1:
5² + 1² = c²
25 + 1 = 26 = c²
c = √26 ≈ 5.1
Repeat this for the lengths BC, CD, and DA.
BC
x-difference = 2
y-difference = 4
4² + 2² = c²
20 = c²
c = √20 ≈ 4.47
CD
x-difference = 5
y-difference = 1
(since this is the same as AB we can use that value ≈ 5.1 )
DA
x-difference = 2
y-difference = 4
(since this is the same as BC, we can use that value ≈ 4.47)
Add all these together:
5.1 + 5.1 + 4.47 + 4.47 ≈ 19.14
(Note: this is not exact, but it's good enough for this purpose)
The closest option to this is B, 19.1 - thus, B is the answer.
