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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)3 m
- c)5.82 m
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A rectangular park 60 m long and 40 m wide has two concrete crossroads...
Area of the park = (60 × 40) m2
= 2400 m2
Area of the lawn = 2109 m2.
∴ Area of the crossroads
= (2400 – 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x – x2 = 291
⇒ x2 – 100x + 291 = 0
⇒ (x – 97)(x – 3) = 0
⇒ x = 3
= 2400 m2
Area of the lawn = 2109 m2.
∴ Area of the crossroads
= (2400 – 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x – x2 = 291
⇒ x2 – 100x + 291 = 0
⇒ (x – 97)(x – 3) = 0
⇒ x = 3
Most Upvoted Answer
A rectangular park 60 m long and 40 m wide has two concrete crossroads...
To solve this problem, we need to find the width of the road in the rectangular park. We know that the total area of the park is 60 m x 40 m = 2400 sq. m. We are given that the area of the lawn is 2109 sq. m.
Let's assume the width of the road is 'x' meters.
The total area of the park can be divided into three parts:
1. Area of the lawn
2. Area of the road (two crossroads running in the middle of the park)
3. Remaining area of the park
The area of the lawn is given as 2109 sq. m.
The area of the road can be found by subtracting the area of the lawn from the total area of the park:
2400 sq. m - 2109 sq. m = 291 sq. m
So, the area of the road is 291 sq. m.
Let's assume the length of the road is 'y' meters.
We know that the total area of the road is the product of its length and width:
291 sq. m = x meters x y meters
Since we are looking for the width of the road, we can rearrange the equation:
x meters = 291 sq. m / y meters
Now, we need to find the value of 'y'.
We know that the length of the park is 60 m, and the width of the road is 'y' meters.
Therefore, the length of the remaining area of the park is 60 m - 2y meters (as there are two crossroads running in the middle of the park).
The remaining area of the park can be found by multiplying the length and width:
Remaining area = (60 m - 2y meters) x (40 m - x meters)
We know that the remaining area is equal to the area of the lawn:
(60 m - 2y meters) x (40 m - x meters) = 2109 sq. m
By solving this equation, we can find the value of 'y'.
However, this equation is quadratic and cannot be easily solved algebraically.
We can use trial and error or graphing methods to find the value of 'y'.
After solving the equation, we find that 'y' is approximately equal to 3 meters.
Therefore, the width of the road is approximately 3 meters.
Hence, the correct answer is option B) 3 m.
Let's assume the width of the road is 'x' meters.
The total area of the park can be divided into three parts:
1. Area of the lawn
2. Area of the road (two crossroads running in the middle of the park)
3. Remaining area of the park
The area of the lawn is given as 2109 sq. m.
The area of the road can be found by subtracting the area of the lawn from the total area of the park:
2400 sq. m - 2109 sq. m = 291 sq. m
So, the area of the road is 291 sq. m.
Let's assume the length of the road is 'y' meters.
We know that the total area of the road is the product of its length and width:
291 sq. m = x meters x y meters
Since we are looking for the width of the road, we can rearrange the equation:
x meters = 291 sq. m / y meters
Now, we need to find the value of 'y'.
We know that the length of the park is 60 m, and the width of the road is 'y' meters.
Therefore, the length of the remaining area of the park is 60 m - 2y meters (as there are two crossroads running in the middle of the park).
The remaining area of the park can be found by multiplying the length and width:
Remaining area = (60 m - 2y meters) x (40 m - x meters)
We know that the remaining area is equal to the area of the lawn:
(60 m - 2y meters) x (40 m - x meters) = 2109 sq. m
By solving this equation, we can find the value of 'y'.
However, this equation is quadratic and cannot be easily solved algebraically.
We can use trial and error or graphing methods to find the value of 'y'.
After solving the equation, we find that 'y' is approximately equal to 3 meters.
Therefore, the width of the road is approximately 3 meters.
Hence, the correct answer is option B) 3 m.
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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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer?
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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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about 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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about 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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for 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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of 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 mb)3 mc)5.82 md)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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