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

The answer is 48 units

Explanation:

Answer 2

48 units

Explanation:

A parallelogram is a polygon with four sides. Opposite sides and opposite angles of a parallelogram are congruent.

The diagonals of a parallelogram bisect each other.

In parallelogram ABCD, AC and DB are the diagonals. Since the diagonals meet at E, hence:

AE = CE and DE = BE (diagonals of a parallelogram bisect each other).

Since AE = CE, hence:

t + 2 = 3t - 14

3t - t = 2 + 14

2t = 16

t = 8 units

Therefore DE = 2t + 8 = 2(8) + 8 = 24 units

DE = BE = 24 units

But DB = DE + BE

DB = 24 + 24

DB = 48 units