△jkl has vertices with the coordinates j(4,5), k(7,9), and l(11,6).
find the approximate perimeter of △jkl using the distance formula. round your answer to the nearest hundredth.
use the keypad to enter the answer in the box.
the perimeter of △jkl is □ units.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $JK$
The distance formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $J(4,5)$ and $K(7,9)$, $x_1 = 4,y_1 = 5,x_2 = 7,y_2 = 9$.
$$
\begin{align*}
JK&=\sqrt{(7 - 4)^2+(9 - 5)^2}\
&=\sqrt{3^2+4^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $KL$
For points $K(7,9)$ and $L(11,6)$, $x_1 = 7,y_1 = 9,x_2 = 11,y_2 = 6$.
$$
\begin{align*}
KL&=\sqrt{(11 - 7)^2+(6 - 9)^2}\
&=\sqrt{4^2+(- 3)^2}\
&=\sqrt{16 + 9}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step3: Calculate the length of $LJ$
For points $L(11,6)$ and $J(4,5)$, $x_1 = 11,y_1 = 6,x_2 = 4,y_2 = 5$.
$$
\begin{align*}
LJ&=\sqrt{(4 - 11)^2+(5 - 6)^2}\
&=\sqrt{(-7)^2+(-1)^2}\
&=\sqrt{49+1}\
&=\sqrt{50}\
&\approx7.07
\end{align*}
$$
## Step4: Calculate the perimeter
Perimeter $P=JK + KL+LJ$. Substitute $JK = 5$, $KL = 5$, and $LJ\approx7.07$ into the formula.
$$
\begin{align*}
P&=5 + 5+7.07\
&=17.07
\end{align*}
$$
# Answer:
$17.07$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(JK\)

Step2: Calculate the length of \(KL\)

Step3: Calculate the length of \(LJ\)

Step4: Calculate the perimeter

Answer: