Question

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8.

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 DB?

20 units
24 units
48 units
68 units

Answer 1

In a parallelogram the diagonals bisect each other, so AE = CE and DE is half of DB.

Set AE = CE:
t + 2 = 3t − 14 → 16 = 2t → t = 8.

Then DE = 2t + 8 = 2(8) + 8 = 24, so DB = 2·DE = 48.

Answer: 48 units.