Question

in parallelogram lonm, what is om? 7 cm 17 cm 24 cm 34 cm

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(OQ = QM\).
Given \(OQ=(2x + 3)\text{cm}\) and \(QM=(3x - 4)\text{cm}\), we set up the equation \(2x+3 = 3x - 4\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(3=x - 4\).
Add \(4\) to both sides: \(x=7\).

Step3: Find the length of \(OM\)

Since \(OM = OQ+QM\) and \(OQ = QM\) (diagonals bisect each other), \(OM = 2\times QM\).
Substitute \(x = 7\) into \(QM=(3x - 4)\text{cm}\), we get \(QM=(3\times7 - 4)\text{cm}=(21 - 4)\text{cm}=17\text{cm}\).
Then \(OM = 2\times17\text{cm}=34\text{cm}\).

Answer:

\(34\text{cm}\)