Chapter 6.6, Problem 25PPS

To determine

The length of WP.

Answer to Problem 25PPS

  $WP=\sqrt{20}$

Explanation of Solution

Given:

WXYZ is a kite.

  

Calculation:

The diagonals of a kite are perpendicular.

According to the Kite Theorem, $\overline{XZ}\perp \overline{WY.}$

The angle XPW is a right angle and hence, the triangle XPW is a right triangle.

So,

  $\begin{array}{l}WP=\sqrt{{\left(WX\right)}^2-{\left(XP\right)}^2}\\ WP=\sqrt{{\left(6\right)}^2-{\left(4\right)}^2}\\ WP=\sqrt{36-16}\\ WP=\sqrt{20}\end{array}$