In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm andPV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

1. Break Down the Problem

To find the length of RS in the parallelogram PQRS, we should note the properties of a parallelogram:

• Opposite sides are equal. Therefore, PS = QR and PQ = RS.

2. Relevant Concepts

Given:

• PS = 7 cm (this side is equal to QR)
• We need to find RS, which is equal to PQ.

From the properties of the parallelogram:

• $PS = QR$
• $PQ = RS$

3. Analysis and Detail

In a parallelogram, we know that:

• Opposite sides are equal in length.
• Therefore, since PS = 7 cm, it follows that QR = 7 cm.

Additionally, since we have no further information about side lengths PQ and RS besides that they are equal, we conclude using the parallelogram's properties.

Consequently, we are mainly interested in confirming the properties hold in this structure.

4. Verify and Summarize

Since PS = 7 cm, it follows that:

• RS must also equal 7 cm, as per the properties of a parallelogram.

Final Answer

The length of RS is 7 cm.