Question

what is the length of segment eb in parallelogram abcd? 30 units 34.5 units 69 units 138 units

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, diagonals bisect each other. So \(DE = EB\) and \(AE=EC\). Here, \(2x + 9=3x - 21\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(2x+9 - 2x=3x - 21-2x\), which gives \(9=x - 21\). Then add \(21\) to both sides: \(x=9 + 21=30\).

Step3: Find length of \(EB\)

Substitute \(x = 30\) into \(3x-21\). So \(EB=3\times30-21=90 - 21=69\).

Answer:

69 units