The perimeter of parallelogram PQSR is 74 cm. What is QS?
4 cm, 6 cm, 8 cm, 12 cm

Solution:

In a parallelogram, the opposite sides are of equal length

PQ = RS

Or PR = QS

So we get

PQ = 4x - 1

RS = 3x + 7

By equating both, we get

4x - 1 = 3x + 7

By further calculation, we get

4x - 3x = 7 + 1

So we get

x = 8

Substituting it we get

PQ = 4 (8) - 1 = 32 - 1

= 31 cm

2 (PQ + QS) = 74

31 + QS = 37

QS = 37 - 31 = 6 cm

Therefore, QS is 6 cm.

Summary:

The perimeter of parallelogram PQSR is 74 cm. QS is 6 cm. In a parallelogram, the opposite sides are of equal length

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