Question

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

Explanation:

Step1: Use the 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 the equation for \(x\)

Subtract \(2x\) from both sides: \(2x+5-2x=4x + 1-2x\), which gives \(5 = 2x+1\).
Subtract \(1\) from both sides: \(5-1=2x+1 - 1\), so \(4=2x\).
Divide both sides by \(2\): \(x=\frac{4}{2}=2\).

Step3: Find the length of \(PQ\)

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

Answer:

\(9\text{cm}\)