Question

quadrilateral vwxy is a kite. what is uv?
y
12
13
x
u
v
w
uv =
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Explanation:

Step1: Recall kite diagonals property

In a kite, one diagonal is the perpendicular bisector of the other. So triangle \(YUV\) is a right triangle with \( \angle U = 90^\circ \), \( YV = 13 \), \( YU = 12 \).

Step2: Apply Pythagorean theorem

For right triangle \(YUV\), \( UV=\sqrt{YV^{2}-YU^{2}} \). Substitute \( YV = 13 \), \( YU = 12 \):
\( UV=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5 \).

Answer:

\( 5 \)