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: Use property of parallelogram diagonals

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

Step2: Solve for t

Subtract t from both sides: $2 = 2t-14$.
Add 14 to both sides: $16 = 2t$.
Divide both sides by 2: $t = 8$.

Step3: Find length of DE

Substitute $t = 8$ into the expression for DE.
$DE=2t + 8=2\times8 + 8=16 + 8=24$.

Step4: Find length of DB

Since the diagonals bisect each other, $DB = 2DE$.
$DB=2\times24 = 48$.

Answer:

48 units