Question

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

Explanation:

1. Recall the property of the diagonals of a parallelogram:

• In a parallelogram, the diagonals bisect each other. So, in parallelogram \(ABCD\) with diagonals \(AC\) and \(BD\) intersecting at \(E\), we have \(AE = EC\) and \(DE=EB\). Also, \(2x + 9=3x - 21\).

1. Solve the equation \(2x + 9 = 3x - 21\) for \(x\):

• First, subtract \(2x\) from both sides of the equation: \(2x+9 - 2x=3x - 21-2x\).
• This gives \(9=x - 21\).
• Then, add 21 to both sides: \(9 + 21=x-21 + 21\), so \(x = 30\).

1. Find the length of \(EB\):

• Substitute \(x = 30\) into the expression for \(EB\) (either \(2x + 9\) or \(3x - 21\)). Let's use \(3x - 21\).
• When \(x = 30\), \(EB=3x - 21=3\times30-21=90 - 21 = 69\).

Answer:

69 units