a grid map marks the plot of harolds garden in meters. the coordinates of the quadrilateral - shaped property are g(-8, 3), a(4, 8), r(10, 0), and d(-2, -5). he wants to build a short fence around the garden. the perimeter of his garden is meters.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $GA$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $G(-8,3)$ and $A(4,8)$, we have $x_1=-8,y_1 = 3,x_2=4,y_2 = 8$.
$$
\begin{align*}
GA&=\sqrt{(4-(-8))^2+(8 - 3)^2}\
&=\sqrt{(12)^2+(5)^2}\
&=\sqrt{144 + 25}\
&=\sqrt{169}\
&=13
\end{align*}
$$
## Step2: Calculate the length of $AR$
For $A(4,8)$ and $R(10,0)$, $x_1=4,y_1 = 8,x_2=10,y_2 = 0$
$$
\begin{align*}
AR&=\sqrt{(10 - 4)^2+(0 - 8)^2}\
&=\sqrt{(6)^2+(-8)^2}\
&=\sqrt{36+64}\
&=\sqrt{100}\
&=10
\end{align*}
$$
## Step3: Calculate the length of $RD$
For $R(10,0)$ and $D(-2,-5)$, $x_1=10,y_1 = 0,x_2=-2,y_2=-5$
$$
\begin{align*}
RD&=\sqrt{(-2 - 10)^2+(-5-0)^2}\
&=\sqrt{(-12)^2+(-5)^2}\
&=\sqrt{144 + 25}\
&=\sqrt{169}\
&=13
\end{align*}
$$
## Step4: Calculate the length of $DG$
For $D(-2,-5)$ and $G(-8,3)$, $x_1=-2,y_1=-5,x_2=-8,y_2 = 3$
$$
\begin{align*}
DG&=\sqrt{(-8-(-2))^2+(3-(-5))^2}\
&=\sqrt{(-6)^2+(8)^2}\
&=\sqrt{36 + 64}\
&=\sqrt{100}\
&=10
\end{align*}
$$
## Step5: Calculate the perimeter
Perimeter $P=GA + AR+RD+DG$
$$
\begin{align*}
P&=13+10 + 13+10\
&=46
\end{align*}
$$
# Answer:
$46$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(GA\)

Step2: Calculate the length of \(AR\)

Step3: Calculate the length of \(RD\)

Step4: Calculate the length of \(DG\)

Step5: Calculate the perimeter

Answer: