Question

quadrilateral tuvw is a kite. what is st? st =

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular and one diagonal bisects the other. Let's assume the diagonals of the kite \(TUVW\) are \(UW\) and \(TV\) which intersect at \(S\). Let \(US = 20\) and \(UT=29\).

Step2: Apply Pythagorean theorem

In right - triangle \(UST\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = UT = 29\) and \(a = US = 20\), and we want to find \(b = ST\). So \(ST=\sqrt{UT^{2}-US^{2}}\).

Step3: Calculate the value

\[

$$\begin{align*} ST&=\sqrt{29^{2}-20^{2}}\\ &=\sqrt{(29 + 20)(29 - 20)}\\ &=\sqrt{49\times9}\\ &=\sqrt{441}\\ &=21 \end{align*}$$

\]

Answer:

21