Question

quadrilateral wxyz is a kite. what is vz? vz =

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular, and one diagonal is bisected by the other. Let the diagonals be \(XZ\) and \(YW\) which intersect at \(V\). Assume \(YW\) bisects \(XZ\).

Step2: Use the Pythagorean theorem

In right - triangle \(VWZ\), if we know the lengths of two sides of the right - triangle formed by the diagonals of the kite. Let's assume we can find \(VZ\) using the Pythagorean theorem. However, since no right - triangle information is clearly given in terms of known side - lengths related to \(VZ\) in a straightforward way, and if we assume that the figure has some hidden property of congruence of triangles formed by the diagonals of the kite. In a kite, the non - congruent sides are adjacent. Let's assume that we can use the fact that the diagonals of a kite are perpendicular. If we consider the right - triangle formed with hypotenuse \(WZ = 73\) and one side \(VW=48\).
By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = WZ\), \(a = VW\) and \(b = VZ\).
We have \(VZ=\sqrt{WZ^{2}-VW^{2}}\).
Substitute \(WZ = 73\) and \(VW = 48\) into the formula:
\[

$$\begin{align*} VZ&=\sqrt{73^{2}-48^{2}}\\ &=\sqrt{(73 + 48)(73 - 48)}\\ &=\sqrt{(121)(25)}\\ &=\sqrt{121}\times\sqrt{25}\\ &=11\times5\\ & = 55 \end{align*}$$

\]

Answer:

55