Question

in parallelogram pqsr, what is pq? 2 cm 5 cm 6 cm 9 cm

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite sides are equal. So, \(PQ = SR\).
Given \(PQ=(2x + 5)\text{cm}\) and \(SR=(4x + 1)\text{cm}\). Then \(2x+5 = 4x + 1\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(5=2x + 1\).
Subtract \(1\) from both sides: \(4 = 2x\).
Divide both sides by \(2\): \(x = 2\).

Step3: Find length of \(PQ\)

Substitute \(x = 2\) into \(PQ=(2x + 5)\text{cm}\).
\(PQ=2\times2+5=4 + 5=9\text{cm}\).

Answer:

\(9\text{cm}\) (the fourth option)