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The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
- a)Rs. 275
- b)Rs. 550
- c)Rs. 600
- d)Rs. 400
- e)Rs. 300
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The width of the path around a square field is 4.5 m and its area is 1...
Let, each side of the field = x
Then, each side with the path = x + 4.5 + 4.5 = x + 9
So, (x + 9)2 - x2 = 105.75
⇒ x2 + 18x + 81 - x2 = 105.75
⇒ 18x + 81 = 105.75
⇒ 18x = 105.75 - 81 = 24.75
⇒ x = 24.75/18 = 11/8
∴ Each side of the square field = 11/8 m
The perimterer = 4 × (11/8) = 11/2 m
So, the total cost of fencing = (11/2) × 100 = Rs. 550
∴ The cost of fencing of the field is Rs. 550
Most Upvoted Answer
The width of the path around a square field is 4.5 m and its area is 1...
Given information:
- Width of the path around the square field = 4.5 m
- Area of the field = 105.75 m²
- Cost of fencing per meter = Rs. 100
Calculations:
1. Area of the inner square:
- Let the side of the inner square be x meters
- Area of the inner square = x * x = x²
2. Area of the outer square:
- Side of the outer square = (x + 2 * 4.5) = (x + 9) meters
- Area of the outer square = (x + 9) * (x + 9) = (x + 9)²
3. Area of the path around the square field:
- Area of the path = Area of the outer square - Area of the inner square
- 105.75 = (x + 9)² - x²
4. Solving for x:
- 105.75 = x² + 18x + 81 - x²
- 18x = 24.75
- x = 1.375
5. Cost of fencing the field:
- Perimeter of the outer square = 4 * (x + 9) = 4 * (1.375 + 9) = 4 * 10.375 = 41.5 m
- Cost of fencing = Perimeter * Cost per meter = 41.5 * 100 = Rs. 4150
- Cost of fencing the field = Rs. 4150 - (4 * 4.5 * 100) = Rs. 4150 - Rs. 1800 = Rs. 2350
Therefore, the correct option is Rs. 2350.
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Community Answer
The width of the path around a square field is 4.5 m and its area is 1...
Let, each side of the field = x
Then, each side with the path = x + 4.5 + 4.5 = x + 9
So, (x + 9)2 - x2 = 105.75
⇒ x2 + 18x + 81 - x2 = 105.75
⇒ 18x + 81 = 105.75
⇒ 18x = 105.75 - 81 = 24.75
⇒ x = 24.75/18 = 11/8
∴ Each side of the square field = 11/8 m
The perimterer = 4 × (11/8) = 11/2 m
So, the total cost of fencing = (11/2) × 100 = Rs. 550
∴ The cost of fencing of the field is Rs. 550
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The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.a)Rs. 275b)Rs. 550c)Rs. 600d)Rs. 400e)Rs. 300Correct answer is option 'B'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.a)Rs. 275b)Rs. 550c)Rs. 600d)Rs. 400e)Rs. 300Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.a)Rs. 275b)Rs. 550c)Rs. 600d)Rs. 400e)Rs. 300Correct answer is option 'B'. Can you explain this answer?.
The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.a)Rs. 275b)Rs. 550c)Rs. 600d)Rs. 400e)Rs. 300Correct answer is option 'B'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.a)Rs. 275b)Rs. 550c)Rs. 600d)Rs. 400e)Rs. 300Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.a)Rs. 275b)Rs. 550c)Rs. 600d)Rs. 400e)Rs. 300Correct answer is option 'B'. Can you explain this answer?.
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