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, 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 by 2: \(t = 8\).

Step3: Find \(DE\)

Substitute \(t = 8\) into \(DE=2t + 8\).
\(DE=2\times8 + 8=16 + 8=24\).

Step4: Find \(DB\)

Since diagonals bisect each other, \(DB = 2DE\).
\(DB=2\times24 = 48\).

Answer:

48 units