Given:
- PQRS is a parallelogram.
- QM is the height from Q to SR.
- QN is the height from Q to PS.
- SR = 12 cm.
- QM = 7.6 cm.

To find:
- The length of QN.

Explanation:

Step 1: Understanding Parallelogram:
A parallelogram is a quadrilateral with opposite sides parallel. In a parallelogram, the opposite sides are equal in length, and the opposite angles are equal in measure.

Step 2: Properties of a Parallelogram:
- Opposite sides are parallel.
- Opposite sides are equal in length.
- Opposite angles are equal.
- Consecutive angles are supplementary (add up to 180 degrees).
- Diagonals bisect each other.

Step 3: Using the Properties:
Since PQRS is a parallelogram, we can use the properties to find the length of QN.

Step 4: Finding the Length of QN:
Since QM is the height from Q to SR, and QN is the height from Q to PS, QM and QN are both perpendicular to their respective bases.

In a parallelogram, the height (perpendicular distance) from a vertex to the opposite side is the same for both pairs of opposite sides.

Therefore, QM = QN.

Since QM is given as 7.6 cm, QN will also be 7.6 cm.

Step 5: Final Answer:
The length of QN is 7.6 cm.

Summary:
- PQRS is a parallelogram.
- QM is the height from Q to SR.
- QN is the height from Q to PS.
- SR = 12 cm.
- QM = 7.6 cm.
- Since QM is the height from Q to SR and QN is the height from Q to PS, QM and QN are both perpendicular to their respective bases.
- In a parallelogram, the height from a vertex to the opposite side is the same for both pairs of opposite sides.
- Therefore, QM = QN.
- The length of QN is 7.6 cm.

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