in parallelogram pqsr, what is pq?\n2 cm\n5 cm\n6 cm\n9 cm

Answer

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So, $PQ = SR$. That is, $2x + 5=4x + 1$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $2x+5 - 2x=4x + 1-2x$, which simplifies to $5 = 2x+1$. Then subtract 1 from both sides: $5 - 1=2x+1 - 1$, getting $4 = 2x$. Divide both sides by 2: $\frac{4}{2}=\frac{2x}{2}$, so $x = 2$.

Step3: Find length of $PQ$

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

Answer:

$9$ cm