The length and breadth of a rectangular park are in the ratio 3:2. A cyclist completes one boundary lap in 8 minutes at 12 km/h. What is the area of the park (in m²)?

Problem restatement
From speed and time, get the perimeter, then use the 3:2 ratio to find actual sides and hence the area.

Given data

• Speed = 12 km/h.
• Lap time = 8 min = 8/60 h = 2/15 h.
• Perimeter P = distance in one lap.
• Length:breadth = 3:2.

Concept/Approach
Distance = speed × time ⇒ P. With 2(L + B) = P and L:B = 3:2, solve for L and B, then area = L × B.

Step-by-Step calculation
P = 12 × (2/15) = 24/15 = 8/5 km = 1.6 km = 1600 mLet L = 3x, B = 2x ⇒ 2(L + B) = 2(5x) = 10x = 1600 ⇒ x = 160L = 480 m, B = 320 mArea = 480 × 320 = 153,600 m²

Verification/Alternative
Perimeter from sides: 2(480 + 320) = 2 × 800 = 1600 m, matching the lap distance.

Common pitfalls
Forgetting to convert km to meters and minutes to hours before multiplying.

Final Answer
153,600 m²