Question

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

Explanation:

Step1: Calculate the side length of the rhombus

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Take points \(Z(5,5)\) and \(W(7,2)\).
\(d=\sqrt{(7 - 5)^2+(2 - 5)^2}=\sqrt{2^2+(-3)^2}=\sqrt{4 + 9}=\sqrt{13}\)

Step2: Calculate the perimeter of the rhombus

Since all sides of a rhombus are equal, perimeter \(P = 4\times\) side length.
\(P=4\times\sqrt{13}=4\sqrt{13}\)

Answer:

\(4\sqrt{13}\) units