Question

what is the perimeter of kite wxyz?
2\sqrt{53}+2 units
2\sqrt{53}+5 units
2\sqrt{53}+10 units
2\sqrt{53}+14 units

Explanation:

Step1: Calculate the length of \( WX \)

Since \( W(-3,3) \) and \( X(2,3) \), using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \), here \( y_1=y_2 = 3 \), so \( WX=\vert-3 - 2\vert=5 \) units.

Step2: Calculate the length of \( XY \)

For \( X(2,3) \) and \( Y(4,-4) \), \( d=\sqrt{(4 - 2)^2+(-4 - 3)^2}=\sqrt{4 + 49}=\sqrt{53} \) units.

Step3: Use the property of a kite

In a kite, two pairs of adjacent sides are equal. So \( WZ = WX = 5 \) units and \( XY=YZ=\sqrt{53} \) units.

Step4: Calculate the perimeter

Perimeter \( P=2XY + 2WX=2\sqrt{53}+2\times5=2\sqrt{53}+10 \) units.

Answer:

\( 2\sqrt{53}+10 \) units (the third option).