Question:
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park, and the rest of the park is used as a lawn. If the area of the lawn is 2109 sq. m, what is the width of the road?
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park, and the rest of the park is used as a lawn. If the area of the lawn is 2109 sq. m, what is the width of the road?
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Road area = 60x + 40x - x^2 (subtracting the double-counted central overlap square); solve the resulting quadratic and reject the unrealistic root.
Updated On: Jul 15, 2026
- 2.91 m
- 3 m
- 5.82 m
- None of these
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Find the total park area and lawn area.
Area of the park \(=60\times40=2400\) m². Area of the lawn \(=2109\) m².
Step 2: Find the area covered by the roads.
Area of the two crossroads \(=2400-2109=291\) m².
Step 3: Set up the equation for the roads' area.
Let the road width be x metres. One road runs the full 60 m length and the other the full 40 m width, and they overlap in a square of \(x \times x\) at the centre (counted twice if added separately), so total road area \(=60x+40x-x^2\).
Step 4: Solve the equation.
\(60x+40x-x^2=291 \Rightarrow x^2-100x+291=0\). Factoring: \((x-97)(x-3)=0\), so \(x=97\) or \(x=3\).
Step 5: Choose the sensible root.
A road width of 97 m is impossible for a park only 40 m wide, so \(x=3\) is the valid answer.
Step 6: Final Answer.
The width of the road is 3 m, so option B is correct.
Area of the park \(=60\times40=2400\) m². Area of the lawn \(=2109\) m².
Step 2: Find the area covered by the roads.
Area of the two crossroads \(=2400-2109=291\) m².
Step 3: Set up the equation for the roads' area.
Let the road width be x metres. One road runs the full 60 m length and the other the full 40 m width, and they overlap in a square of \(x \times x\) at the centre (counted twice if added separately), so total road area \(=60x+40x-x^2\).
Step 4: Solve the equation.
\(60x+40x-x^2=291 \Rightarrow x^2-100x+291=0\). Factoring: \((x-97)(x-3)=0\), so \(x=97\) or \(x=3\).
Step 5: Choose the sensible root.
A road width of 97 m is impossible for a park only 40 m wide, so \(x=3\) is the valid answer.
Step 6: Final Answer.
The width of the road is 3 m, so option B is correct.
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