in the diagram, zy = wx = 2\\sqrt{10}. what is the perimeter of rectangle wxyz?\n\\(\\sqrt{10}\\)…

Explanation:

Step1: Recall rectangle property

In a rectangle, opposite - sides are equal. Given (ZY = WX=2\sqrt{10}), and (ZW = XY).

Step2: Use the distance formula (d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}) to find (ZW)

Let (Z(-9,5)) and (W(-6,6)). Then (x_1=-9,y_1 = 5,x_2=-6,y_2 = 6). [ \begin{align*} ZW&=\sqrt{(-6+9)^2+(6 - 5)^2}\ &=\sqrt{3^2+1^2}\ &=\sqrt{9 + 1}\ &=\sqrt{10} \end{align*} ] Since (ZW = XY=\sqrt{10})

Step3: Calculate the perimeter (P) of the rectangle

The perimeter formula of a rectangle is (P = 2(l + w)), where (l) and (w) are the length and width. Here, (l = 2\sqrt{10}) and (w=\sqrt{10}) [ \begin{align*} P&=2(2\sqrt{10}+\sqrt{10})\ &=2\times3\sqrt{10}\ &=6\sqrt{10} \end{align*} ]

Answer:

(6\sqrt{10}) units