Question

in parallelogram lonm, what is om? (2x + 3) cm, (3x - 4) cm, options: 7 cm, 17 cm, 24 cm, 34 cm

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, diagonals bisect each other. So \( OQ = QM \), which means \( 2x + 3 = 3x - 4 \).

Step2: Solve for \( x \)

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

Step3: Find \( OQ \) and \( QM \)

Substitute \( x = 7 \) into \( 2x + 3 \): \( 2(7) + 3 = 14 + 3 = 17 \) cm. So \( OQ = QM = 17 \) cm.

Step4: Calculate \( OM \)

Since \( OM = OQ + QM \), \( OM = 17 + 17 = 34 \) cm.

Answer:

34 cm