Question

in parallelogram pqsr, what is pq?
options: 2 cm, 5 cm, 6 cm, 9 cm
the parallelogram has sides: pq is (2x + 5) cm, rs is (4x + 1) cm

Explanation:

Step1: Use parallelogram opposite sides property

In a parallelogram, opposite sides are equal, so $PQ = RS$. Substitute the given expressions:
$2x + 5 = 4x + 1$

Step2: Solve for x

Rearrange the equation to isolate x:
$5 - 1 = 4x - 2x$
$4 = 2x$
$x = \frac{4}{2} = 2$

Step3: Calculate length of PQ

Substitute $x=2$ into the expression for PQ:
$PQ = 2(2) + 5$

Answer:

9 cm