Question

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

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, opposite - sides are equal. So, $PQ = RS$.
We have $PQ=(2x + 5)$ cm and $RS=(4x + 1)$ cm. Then $2x+5 = 4x + 1$.

Step2: Solve the equation for x

Subtract $2x$ from both sides: $5=4x + 1-2x$, which simplifies to $5 = 2x+1$.
Subtract 1 from both sides: $5 - 1=2x$, so $4 = 2x$.
Divide both sides by 2: $x = 2$.

Step3: Find the length of PQ

Substitute $x = 2$ into the expression for $PQ$. $PQ=2x + 5$.
$PQ=2\times2+5=4 + 5=9$ cm.

Answer:

$9$ cm