Question

the gazebo in the town square has a pentagonal roof, as shown. around the edges of the roof, the mayors staff is installing decorative rope lighting so that the gazebo can be used for nighttime events. what length of rope lighting do they need to outfit the entire roof edge? enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the pentagon: blank inches

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Find distance between J(-1,-1) and C(27,-20)

$d_{JC}=\sqrt{(27-(-1))^2+((-20)-(-1))^2}=\sqrt{(27 + 1)^2+(-20 + 1)^2}=\sqrt{28^2+(-19)^2}=\sqrt{784 + 361}=\sqrt{1145}\approx33.84$.
Since we need to find the perimeter of the pentagon and only one - side distance is given in a way that we can calculate, and no other side - length information is provided, we assume we need to find the length of this one side as a part of the perimeter calculation. If we had all the side - lengths calculated using the distance formula for each pair of adjacent vertices of the pentagon, we would sum them up. But with only this information, we assume the question is asking for the length of this particular side for now.

Answer:

Approximately 33.84 inches