Question

in the diagram, ( zy = wx = 2sqrt{10} ). what is the perimeter of rectangle ( wxyz )?
( \bigcirc ) ( sqrt{10} ) units
( \bigcirc ) ( 2sqrt{10} ) units
( \bigcirc ) ( 6sqrt{10} ) units
( \bigcirc ) ( 8sqrt{10} ) units

Explanation:

Step1: Find length of XY

Use distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)}$
For $X(-4,0)$ and $Y(-7,-1)$:
$$XY=\sqrt{(-7-(-4))^2+(-1-0)^2}=\sqrt{(-3)^2+(-1)^2}=\sqrt{9+1}=\sqrt{10}$$

Step2: Recall rectangle perimeter formula

Perimeter $P=2(l+w)$, where $l=ZY=2\sqrt{10}$, $w=XY=\sqrt{10}$

Step3: Calculate perimeter

$$P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}$$

Answer:

$\boldsymbol{6\sqrt{10}}$ units (matches the third option)