Question

In the parallelogram shown, AE = p − 8, CE = 2p − 58, and DE = p + 15.

Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E.

What is the length of line segment EB?

42 units
50 units
65 units
73 units

Answer 1

In a parallelogram the diagonals bisect each other, so AE = CE and DE = BE.

Set AE = CE: p − 8 = 2p − 58 → p = 50.

Then EB = DE = p + 15 = 50 + 15 = 65 units.

Answer: 65 units.