Question

the graph shows the endpoints of one side of a parallelogram. determine the perimeter of the parallelogram. enter the unknown segment length(s), then calculate the perimeter of the polygon. perimeter of the parallelogram: units

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: Calculate length of side WO

For points $W(1,-3)$ and $O(30,-2)$, $x_1 = 1,y_1=-3,x_2 = 30,y_2=-2$.
$d_{WO}=\sqrt{(30 - 1)^2+(-2+3)^2}=\sqrt{29^2 + 1^2}=\sqrt{841+1}=\sqrt{842}\approx29.02$.

Step3: Recall property of parallelogram

In a parallelogram, opposite sides are equal. Given one side length (say $BO = 18.68$), the opposite - side length is also $18.68$, and the other pair of opposite - sides have length approximately $29.02$.

Step4: Calculate perimeter

The perimeter $P$ of a parallelogram with side lengths $a$ and $b$ is $P = 2(a + b)$. Here $a = 18.68$ and $b\approx29.02$.
$P=2(18.68 + 29.02)=2\times47.7=95.4$.

Answer:

$95.4$