Question

quadrilateral stuv is a kite. what is rs? rs =

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(VRS\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = VS=65\) and \(b = VR = 56\), and \(a=RS\).
So, \(RS=\sqrt{VS^{2}-VR^{2}}\)

Step2: Substitute values

Substitute \(VS = 65\) and \(VR = 56\) into the formula:
\(RS=\sqrt{65^{2}-56^{2}}=\sqrt{(65 + 56)(65 - 56)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\))
\(=\sqrt{121\times9}=\sqrt{121}\times\sqrt{9}\)
\(=11\times3\)

Answer:

\(33\)