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A rectangular park 60 metre long and 40 metre 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 metre² then the width of the road is
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- 3 metre
- 5 metre
- 6 metre
- 2 metre
- 3 metre
Correct Option: A
Area of rectangular park = 60 × 40 = 2400 sq. metre
Let the width of cross-road be x metre.
∴ Area of cross-roads = 60x + 40x – x²
= 100x – x²
According to the question,
100x – x² = 2400 – 2109
⇒ 100x – x² = 291
⇒ x² – 100x + 291 = 0
⇒ x² – 3x – 97x + 291 = 0
⇒ x (x – 3) – 97 (x – 3) = 0
⇒ (x – 3) (x – 97) = 0
⇒ x = 3 because x ≠ 97
