Question
Construct a quadrilateral PQRS, in which $\angle\text{PQR}=45^\circ,$ $\angle\text{QRS}=90^\circ,$ $QR = 5\ cm, PQ = 9\ cm$ and $Rs = 7\ cm.$
✓
Answer
Steps of construction:
Step $I$: Draw $QR = 5\ cm.$
Step $II$: Construct $\angle\text{PQR}=45^\circ$ at $Q$.
Step $III$: With $Q$ as the centre and radius $9\ cm$, cut off $QP = 9\ cm$.
Step $IV$: Construct $\angle\text{QRS}=90^\circ$ at $R$.
Step $V$: With $R$ as the centre and radius $7\ cm$, cut off $RS = 7\ cm.$ Since, the line segment $PQ$ and $RS$ intersect each other, the quadrilateral cannot be constructed.
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