1. **Problem Statement**: Given line segment $PQ=7$ cm, construct triangle $PQR$ so that $QR=6$ cm and $\angle RPQ=60^\circ$. Then construct the perpendicular to $PR$ passing through $Q$ and measure the perpendicular distance from $Q$ to line $PR$. 2. **Step 1: Draw line segment PQ** - Using a ruler, draw line segment $PQ$ with length $7$ cm. 3. **Step 2: Construct angle $\angle RPQ = 60^\circ$ at point P** - Place compass point at $P$, draw an arc crossing line $PQ$. - Without changing compass width, from the intersection on $PQ$, draw another arc intersecting the first arc. - Draw line from $P$ through the intersection of arcs; this forms a $60^\circ$ angle at $P$. 4. **Step 3: Mark point R on the ray from P at $60^\circ$** - With compass width $6$ cm, place compass at $Q$ and arc over the area. - Also, with compass at $P$ on the $60^\circ$ ray, mark point $R$ such that $QR=6$ cm. 5. **Step 4: Connect points R and Q** - Draw line segment $RQ$ to complete triangle $PQR$ with required measurements. 6. **Step 5: Construct perpendicular to $PR$ passing through $Q$** - Place compass at $Q$ with a radius intersecting $PR$ in two points. - From these two points, draw arcs intersecting above and below $PR$. - Draw the perpendicular line through these intersections passing through $Q$. 7. **Step 6: Measure perpendicular distance from Q to line PR** - This distance equals the length of the perpendicular segment from $Q$ to $PR$. - Use ruler to measure this length precisely. **Final Answer:** - Triangle $PQR$ constructed with $PQ=7$ cm, $QR=6$ cm, and $\angle RPQ=60^\circ$. - Perpendicular to $PR$ through $Q$ constructed. - Perpendicular distance measured using ruler (numerical value depends on actual drawing).