Question

quadrilateral wxyz is a kite. what is vx? 20 12 vx =

Explanation:

Step1: Recall kite - property

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

Step2: Use the Pythagorean theorem in right - triangle \(WXV\)

In right - triangle \(WXV\), we know that \(WX = 20\) and \(WV=12\). Let \(VX = a\). By the Pythagorean theorem \(WX^{2}=WV^{2}+VX^{2}\), that is \(a^{2}=WX^{2}-WV^{2}\).

Step3: Substitute the given values

Substitute \(WX = 20\) and \(WV = 12\) into the formula \(a^{2}=WX^{2}-WV^{2}\). We get \(a^{2}=20^{2}-12^{2}=400 - 144=256\).

Step4: Solve for \(VX\)

Take the square root of both sides of the equation \(a^{2}=256\). Since \(a>0\) (as it represents the length of a line - segment), \(a = 16\).

Answer:

16