Question

quadrilateral vwxy is a kite. what is uv? y 12 x 13 u v w uv = \boxed{}

Explanation:

Step1: Recall kite properties

In a kite, one diagonal is the perpendicular bisector of the other, and the two triangles formed by a diagonal are congruent. Also, the diagonals intersect at right angles. So triangle YUV is a right triangle with hypotenuse YV = 13 and one leg YU = 12.

Step2: Apply Pythagorean theorem

For a right triangle with hypotenuse \( c \) and legs \( a, b \), \( a^{2}+b^{2}=c^{2} \). Let \( UV = x \), \( YU = 12 \), \( YV = 13 \). Then \( x^{2}+12^{2}=13^{2} \).

Step3: Solve for x

\( x^{2}=13^{2}- 12^{2}=169 - 144 = 25 \). Taking square root, \( x = 5 \) (since length is positive).

Answer:

5