Question

use the figure shown for items 4–5.
if ( wy + xz = 28 ), what is ( pz )?
( pz = square )

Explanation:

Step1: Recall properties of parallelograms

In a parallelogram, the diagonals bisect each other. So, \( WP = PY \) and \( XP = PZ \). Also, we know \( WY \) and \( XZ \) are diagonals, and from the figure, \( WP = 8 \), so \( WY = 2\times WP = 2\times8 = 16 \).

Step2: Find length of \( XZ \)

Given \( WY + XZ = 28 \), substitute \( WY = 16 \):
\( 16 + XZ = 28 \)
Subtract 16 from both sides: \( XZ = 28 - 16 = 12 \).

Step3: Find \( PZ \)

Since diagonals bisect each other, \( PZ=\frac{1}{2}XZ \).
Substitute \( XZ = 12 \): \( PZ=\frac{1}{2}\times12 = 6 \).

Answer:

\( 6 \)