Question

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

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate length of MN

For points $M(2,3)$ and $N(3,4)$, $d_{MN}=\sqrt{(3 - 2)^2+(4 - 3)^2}=\sqrt{1 + 1}=\sqrt{2}$.

Step3: Calculate length of NK

For points $N(3,4)$ and $K(5,3)$, $d_{NK}=\sqrt{(5 - 3)^2+(3 - 4)^2}=\sqrt{4+1}=\sqrt{5}$.

Step4: Use kite - property

In a kite, two pairs of adjacent sides are equal. So, $MN = ML=\sqrt{2}$ and $NK=KL=\sqrt{5}$.

Step5: Calculate perimeter

Perimeter $P = 2\sqrt{2}+2\sqrt{5}$.

Answer:

$2\sqrt{2}+2\sqrt{5}$ units