what is the perimeter of kite klmn?
√2 + √5 units
√14 units
2√2 + 2√5 units
4√5 units

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $MN$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $M(2,3)$ and $N(3,4)$, $x_1 = 2,y_1 = 3,x_2=3,y_2 = 4$.
$$
\begin{align*}
MN&=\sqrt{(3 - 2)^2+(4 - 3)^2}\
&=\sqrt{1^2+1^2}\
&=\sqrt{1 + 1}\
&=\sqrt{2}
\end{align*}
$$
## Step2: Calculate the length of $NK$
For $N(3,4)$ and $K(5,3)$, $x_1 = 3,y_1 = 4,x_2=5,y_2 = 3$.
$$
\begin{align*}
NK&=\sqrt{(5 - 3)^2+(3 - 4)^2}\
&=\sqrt{2^2+(- 1)^2}\
&=\sqrt{4 + 1}\
&=\sqrt{5}
\end{align*}
$$
## Step3: Use the property of a kite
In a kite, two pairs of adjacent sides are equal. So $MN = ML=\sqrt{2}$ and $NK=KL=\sqrt{5}$.
The perimeter $P=2MN + 2NK$.
$$
\begin{align*}
P&=2\sqrt{2}+2\sqrt{5}
\end{align*}
$$

# Answer:
$2\sqrt{2}+2\sqrt{5}$ units (i.e., the third option)

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(MN\)

Step2: Calculate the length of \(NK\)

Step3: Use the property of a kite

Answer: