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: $2x+5-2x=4x + 1-2x$ $5 = 2x+1$. Subtract 1 from both sides: $5 - 1=2x+1 - 1$ $4 = 2x$. Divide both sides by 2: $\frac{4}{2}=\frac{2x}{2}$ $x = 2$.

Step3: Find the length of PQ

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

Answer:

9 cm