Question: Construct a parlelogram $pqrs$ in which $PQ$ is equal to $5.8$ CM, $P$ is equal to $4.5$ cm and $QS$ is equal to $6.2$ CM

1. **Problem Statement:** Construct a parallelogram $PQRS$ where side $PQ = 5.8$ cm, side $PS = 4.5$ cm, and diagonal $QS = 6.2$ cm. 2. **Important Properties:** - Opposite sides of a parallelogram are equal and parallel. - Diagonals bisect each other. 3. **Step-by-step Construction:** 1. Draw a line segment $PQ$ of length $5.8$ cm. 2. At point $P$, construct an angle to draw side $PS$ of length $4.5$ cm. 3. Mark point $S$ such that $PS = 4.5$ cm. 4. Draw a circle centered at $Q$ with radius $6.2$ cm (length of diagonal $QS$). 5. Draw a circle centered at $P$ with radius equal to the length of diagonal $PR$ (which equals $QS$ in parallelogram). Since $QS = 6.2$ cm, $PR$ also equals $6.2$ cm. 6. The intersection of these two circles gives point $R$. 7. Connect points $S$ and $R$ to complete parallelogram $PQRS$. 4. **Verification:** - Check that $PQ = SR = 5.8$ cm. - Check that $PS = QR = 4.5$ cm. - Check that diagonals $QS$ and $PR$ both equal $6.2$ cm. This completes the construction of parallelogram $PQRS$ with the given dimensions.