what is the perimeter of rectangle efgh?
√10 + √29 units
2√10 + 2√29 units
22 units
39 units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $EF$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $E(1,-1)$ and $F(- 4,1)$, $x_1 = 1,y_1=-1,x_2=-4,y_2 = 1$.
$$
\begin{align*}
EF&=\sqrt{(-4 - 1)^2+(1+1)^2}\
&=\sqrt{(-5)^2+2^2}\
&=\sqrt{25 + 4}\
&=\sqrt{29}
\end{align*}
$$
## Step2: Calculate the length of $FG$
For points $F(-4,1)$ and $G(-3,4)$, $x_1=-4,y_1 = 1,x_2=-3,y_2 = 4$.
$$
\begin{align*}
FG&=\sqrt{(-3 + 4)^2+(4 - 1)^2}\
&=\sqrt{1^2+3^2}\
&=\sqrt{1+9}\
&=\sqrt{10}
\end{align*}
$$
## Step3: Use the property of rectangle (opposite sides are equal)
The perimeter $P$ of rectangle $EFGH$ is $P = 2(EF+FG)$.
$$
\begin{align*}
P&=2(\sqrt{29}+\sqrt{10})\
&=2\sqrt{10}+2\sqrt{29}
\end{align*}
$$

# Answer:
$2\sqrt{10}+2\sqrt{29}\text{ units}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(EF\)

Step2: Calculate the length of \(FG\)

Step3: Use the property of rectangle (opposite sides are equal)

Answer: