Question

in the parallelogram shown, ae = t + 2, ce = 3t - 14, and de = 2t + 8. what is the length of line segment db? 20 units 24 units 48 units 68 units

Explanation:

Step1: Set AE equal to CE

In a parallelogram, diagonals bisect each other, so $AE = CE$.
$t + 2 = 3t - 14$

Step2: Solve for t

Rearrange to isolate t.
$2 + 14 = 3t - t$
$16 = 2t$
$t = \frac{16}{2} = 8$

Step3: Find length of DE

Substitute t=8 into DE's expression.
$DE = 2(8) + 8 = 16 + 8 = 24$

Step4: Calculate length of DB

Diagonals bisect each other, so $DB = 2 \times DE$.
$DB = 2 \times 24 = 48$

Answer:

48 units