Question

in parallelogram pqsr, what is pq? 2 cm 5 cm 6 cm 9 cm (2x + 5) cm (4x + 1) cm

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, opposite sides are equal. So, \(PQ = RS\).
Given \(PQ=(2x + 5)\) cm and \(RS=(4x + 1)\) cm. So, we set up the equation: \(2x+5 = 4x + 1\).

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 \(PQ=(2x + 5)\) cm.
\(PQ=2(2)+5=4 + 5=9\) cm? Wait, no, wait. Wait, maybe I mixed up. Wait, in parallelogram PQSR, PQ and RS are opposite sides? Wait, no, maybe PQ and SR? Wait, the diagram: PQ is (2x+5), RS is (4x+1). Wait, but when x=2, 2x+5=9, 4x+1=9. But the options are 2,5,6,9. Wait, but let's check again. Wait, maybe I made a mistake. Wait, maybe PQ and PS? No, no, in parallelogram, opposite sides are equal. So PQ and RS should be equal. Wait, but let's re - solve the equation. \(2x+5=4x + 1\)
\(5 - 1=4x-2x\)
\(4 = 2x\)
\(x = 2\)
Then PQ=2x + 5=2*2+5=9. But the option is 9. Wait, but maybe the diagram is different. Wait, maybe PQ is (2x + 5) and another side? Wait, no, the question is "In parallelogram PQSR, what is PQ?". The options are 2cm,5cm,6cm,9cm. So when x=2, PQ=9cm. But wait, let's check again. Wait, maybe I had the opposite sides wrong. Suppose PQ and SR are equal, but maybe the labels are different. Wait, no, the equation \(2x + 5=4x+1\) gives x=2, then PQ=9. So the answer should be 9cm.

Answer:

9 cm