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 the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(AE = CE\).

$$t + 2=3t - 14$$

Step2: Solve the equation 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 the length of \(DE\)

Substitute \(t = 8\) into \(DE=2t + 8\)

$$DE=2\times8 + 8=16 + 8=24$$

Step4: Find the length of \(DB\)

Since the diagonals bisect each other, \(DB = 2DE\)

$$DB=2\times24 = 48$$

Answer:

48 units