Question

in the parallelogram shown, ae = p - 8, ce = 2p - 58, and de = p + 15. what is the length of line segment eb? 73 units 42 units 65 units 50 units

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, diagonals bisect each other. So, \( AE = CE \).
Set \( p - 8 = 2p - 58 \).

Step2: Solve for \( p \)

Subtract \( p \) from both sides: \( -8 = p - 58 \).
Add 58 to both sides: \( p = 50 \).

Step3: Find \( DE \) length

Given \( DE = p + 15 \), substitute \( p = 50 \): \( DE = 50 + 15 = 65 \).

Step4: Use diagonals bisect property for \( EB \)

In a parallelogram, diagonals bisect each other, so \( EB = DE \). Thus, \( EB = 65 \) units.

Answer:

65 units (corresponding to the option with 65 units)