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

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $ XY $
Use the distance formula $ d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} $.
For $ X(-4,0) $ and $ Y(-7,-1) $, $ x_1=-4,y_1 = 0,x_2=-7,y_2=-1 $.
$$
\begin{align*}
XY&=\sqrt{(-7+4)^2+(-1 - 0)^2}\
&=\sqrt{(-3)^2+(-1)^2}\
&=\sqrt{9 + 1}\
&=\sqrt{10}
\end{align*}
$$
## Step2: Calculate the perimeter of the rectangle
The perimeter formula of a rectangle is $ P=2(l + w) $.
Given $ l = 2\sqrt{10} $ ( $ WX=ZY = 2\sqrt{10} $) and $ w=\sqrt{10} $ ( $ XY=WZ=\sqrt{10} $).
$$
\begin{align*}
P&=2(2\sqrt{10}+\sqrt{10})\
&=2\times3\sqrt{10}\
&=6\sqrt{10}
\end{align*}
$$

# Answer:
$ 6\sqrt{10}\text{ units} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \( XY \)

Step2: Calculate the perimeter of the rectangle

Answer: