Question

in the diagram, zy = wx = 2√10. what is the perimeter of rectangle wxyz? 8√10 units √10 units 2√10 units 6√10 units

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ and $w$ are the length and width. In rectangle $WXYZ$, $ZY = WX=2\sqrt{10}$ and $ZW = XY$.

Step2: Calculate length of $ZW$ using distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $Z(-9,5)$ and $W(-6,6)$, $x_1=-9,y_1 = 5,x_2=-6,y_2 = 6$. Then $ZW=\sqrt{(-6+9)^2+(6 - 5)^2}=\sqrt{3^2+1^2}=\sqrt{9 + 1}=\sqrt{10}$.

Step3: Calculate the perimeter

Since $l = 2\sqrt{10}$ and $w=\sqrt{10}$, $P=2(2\sqrt{10}+\sqrt{10})=2\times3\sqrt{10}=6\sqrt{10}$.

Answer:

$6\sqrt{10}$ units