A 60 m × 40 m rectangular park has two equal-width concrete roads crossing through its centre (one along length, one along breadth). The rest is lawn. If the lawn area is 2109 m², what is the width of each road?

Problem restatementTwo perpendicular roads of equal width w run through the middle of a 60 m by 40 m park. Lawn area (park minus roads) is 2109 m². Find w.

Given data

• Total area = 60 × 40 = 2400 m²
• Road area = 60w + 40w − w² (subtracting the overlapping square once)
• Lawn area = 2109 m²

Concept/ApproachSet total area minus road area equal to the lawn area and solve the quadratic in w.

Step-by-Step calculation2400 − (100w − w²) = 2109w² − 100w + 2400 − 2109 = 0w² − 100w + 291 = 0Discriminant = 10000 − 1164 = 8836 = 94²w = [100 ± 94] / 2 ⇒ w = 3 or 97Feasible width < 40 ⇒ w = 3 m

Verification/AlternativeRoad area = 60×3 + 40×3 − 3×3 = 180 + 120 − 9 = 291; Lawn = 2400 − 291 = 2109.

Common pitfallsForgetting to subtract the intersection area w² that gets double-counted.

Final Answer3 m