Construct a rectangle PQRS given that PQ=5 cm and the diagonal PR=6.5 cm.

Answer

To construct a rectangle PQRS given that PQ = 5 cm and the diagonal PR = 6.5 cm, follow these steps:

### Step-by-Step Solution:

1. **Draw the Base PQ**:
- Using a ruler, draw a line segment PQ that measures 5 cm. Label the endpoints as P and Q.

**Hint**: Ensure that you measure accurately using the ruler for a precise length of 5 cm.

2. **Construct a Right Angle at Point Q**:
- At point Q, use a protractor to measure a 90-degree angle. Draw a line upwards from Q. This will be the line QS.

**Hint**: Remember that a rectangle has all right angles, so it’s important to get this angle correct.

3. **Locate Point R**:
- From point Q, measure a length of 6.5 cm along the line you just drew (QS) and mark this point as R.

**Hint**: Use the ruler to measure 6.5 cm accurately from Q to find R.

4. **Construct a Right Angle at Point P**:
- At point P, use the protractor again to measure a 90-degree angle. Draw a line upwards from P. This will be the line PS.

**Hint**: This line should be perpendicular to PQ, just like QS.

5. **Locate Point S**:
- From point P, measure a length of 6.5 cm along the line you just drew (PS) and mark this point as S.

**Hint**: Ensure that the length PS is also 6.5 cm to maintain the rectangle's properties.

6. **Connect Points R and S**:
- Finally, connect points R and S with a straight line. This completes the rectangle PQRS.

**Hint**: Double-check that both sides PQ and SR are equal (5 cm) and that both diagonals PR and QS are equal (6.5 cm).

### Summary of Steps:
1. Draw PQ = 5 cm.
2. Construct a right angle at Q.
3. Measure 6.5 cm from Q to locate R.
4. Construct a right angle at P.
5. Measure 6.5 cm from P to locate S.
6. Connect R and S to complete the rectangle.