Chapter 6.4, Problem 39PPS

To determine

The length of YW.

Answer to Problem 39PPS

  $YW=5$

Explanation of Solution

Given:

WXYZ is a rectangle.

  $XW=3,WZ=4,XZ=b$

Calculation:

Using the Pythagoras Theorem to find the length of line XZ:

Now,

  $\begin{array}{l}XZ=\sqrt{{\left(XW\right)}^2+{\left(WZ\right)}^2}\\ XZ=\sqrt{3^2+4^2}\\ XZ=\sqrt{25}\\ XZ=5\end{array}$

Also, YW = XZ, as the diagonals of rectangle are congruent.

  $\begin{array}{l}YW=XZ\\ YW=5\end{array}$