A rectangular park 60 m long and 40 m wide has two concrete crossroads running…
2024
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
- A.
2.91 m
- B.
2.91 m
- C.
3 m
- D.
None of these
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Solution: Find the width of each road.
Let x be the width (in metres) of each road.
Area of the park = 60 × 40 = 2400 m².
Area covered by the two perpendicular roads = 60x + 40x − x² = 100x − x² (the intersection x² is counted twice so subtract once).
Lawn area = total area − roads area = 2400 − (100x − x²) = x² − 100x + 2400.
Set this equal to the given lawn area 2109: x² − 100x + 2400 = 2109 ⇒ x² − 100x + 291 = 0.
Solve the quadratic: discriminant = 10000 − 4×1×291 = 8836 = 94², so x = (100 ± 94)/2 ⇒ x = 3 or x = 97.
Reject 97 m as impractical (larger than park dimensions).
Therefore the width of each road is 3 m.