Chapter 6.4, Problem 15PPS

To determine

The length of ZP.

Answer to Problem 15PPS

  $ZP=43$

Explanation of Solution

Given:

WXYZ is a rectangle.

  $PY=3x-5\text{, WP = 2x + 11 }$

Calculation:

The diagonals of a parallelogram bisect each other.

According to the Diagonals of Parallelogram Theorem, P is the midpoint of line WY.

So,

  $\overline{PY}\cong \overline{WP}$

Hence,

  $\begin{array}{l}PY=WP\\ 3x-5=2x+11\\ 3x-2x=11+5\\ x=16\end{array}$

The length of PY will be:

  $\begin{array}{l}PY=3x-5\\ PY=3\left(16\right)-5\\ PY=43\end{array}$

When a parallelogram is also a rectangle, its diagonals are congruent and also bisect each other.

According to the Diagonals of Rectangle Theorem;

  $\overline{ZP}\cong \overline{PY}$

So,

  $\begin{array}{l}ZP=PY\\ ZP=43\end{array}$