Find the perimeter of the polygon defined by the coordinates (5, 8), (12, 0), (-5, 0), and (-1, 8). (round to nearest tenth) a) 42.5 units b) 42.6 units c) 47.5 units d) 47.6 units

The correct option is A

Step-by-step explanation:

The perimeter of a triangle is equal to the sum of the length of the 4 sides.

The vertex is:

(5,8), (12,0), (-5,0), (-1,8)

first, we see wich vertex have one element in common:

(5,8) and (-1, 8)

heer we have y = 8 constant, so this creates a line parallel to the x-axis.

The distance between these two vectors is:

(5, 8) - (-1, 8) = (6, 0)

the other ones with a term in common are:

d = √(6^2 + 0^2) = 6

(12, 0) and (-5, 0)

This also creates a parallel line to the x-axis.

the distance is:

(12,0) - (-5, 0) = (17, 0)

the distance is:

d = √(17^2 + 0^2) = 17

now, from the two pairs we have, we select the sides that are more close to the other (one where y = 0 and other where y = 8, because we now are looking for the lines that conect the two parallel lines we already described)  and we need to search for the clossest ones because in this way we ensure that the lines created between the vertex do not cross with eachother.

Those are:

(5,8) and (12,0)

The distance is:

(5,8) - (12,0) = (12 - 5, 8) = (7,8)

d = √(7^2 + 8^2) = 10.6

The other side is between the vertex:

(-5, 0) abd (-1, 8)

the distance is:

(-5, 0) - (-1, 8) = (-5 + 1, - 8) = (-4, -8)

d = √(/-4)^2 + (-8)^2) = 8.9

The perimeter is:

P = 8.9 + 10.6 + 17 + 6 = 42.5