Question

what is the perimeter of rhombus wxyz? 12 units 4√13 units 20 units √13 units

Explanation:

Step1: Recall property of rhombus

All sides of a rhombus are equal. So, find the length of one - side using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate the length of side WZ

Let $W(7,2)$ and $Z(5,5)$. Then $x_1 = 7,y_1 = 2,x_2 = 5,y_2 = 5$.
$d=\sqrt{(5 - 7)^2+(5 - 2)^2}=\sqrt{(-2)^2+3^2}=\sqrt{4 + 9}=\sqrt{13}$.

Step3: Calculate the perimeter

Since all sides of a rhombus are equal and perimeter $P = 4s$ (where $s$ is the side - length), $P = 4\sqrt{13}$.

Answer:

$4\sqrt{13}$ units