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The ratio between the length and the breadth of a rectangular park is 3 : 2 If a man cycling along the boundary of the park at the speed of 12km/hr completes one round it 8 minutes, then the area of the park (in sq. m) is :
- a)15360
- b)153600
- c)30720
- d)307200
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The ratio between the length and the breadth of a rectangular park is...
Perimeter = Distance covered in 8 min.
= 
Let length = 3x metres and breadth = 2x metres.
Then, 2 (3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 × 320)m2 = 153600 m2
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Community Answer
The ratio between the length and the breadth of a rectangular park is...
Given:
- The ratio between the length and breadth of the rectangular park is 3:2.
- The man completes one round of the park in 8 minutes.
- The man's speed is 12 km/hr.
To find:
The area of the park in square meters.
Solution:
Step 1: Determine the Dimensions of the Park
Let the length of the park be 3x and the breadth be 2x (as given in the ratio).
Step 2: Calculate the Perimeter of the Park
The perimeter of the rectangular park is the distance covered by the man in one round.
Since the man's speed is given in km/hr and the time taken to complete one round is given in minutes, we need to convert the time to hours.
Given: Time taken to complete one round = 8 minutes
1 hour = 60 minutes
Therefore, 8 minutes = 8/60 = 2/15 hours
The distance covered in one round (perimeter) is given by the formula:
Perimeter = Speed × Time
Given: Speed = 12 km/hr
Time = 2/15 hours
Perimeter = 12 × (2/15) = 24/15 km
Step 3: Convert the Perimeter to meters
1 km = 1000 m
Therefore, 24/15 km = (24/15) × 1000 = 1600/15 = 320/3 m
Step 4: Calculate the Length and Breadth of the Park
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + breadth)
Given: Perimeter = 320/3 m
Using the above formula:
320/3 = 2(3x + 2x)
320/3 = 2(5x)
320/3 = 10x
x = (320/3) / 10 = 32/3
Length of the park = 3x = 3 × (32/3) = 32 m
Breadth of the park = 2x = 2 × (32/3) = 64/3 m
Step 5: Calculate the Area of the Park
Area of a rectangle is given by the formula:
Area = length × breadth
Area = (32) × (64/3) = 2048/3 = 682.67 sq.m (approximately)
Therefore, the area of the park is approximately 682.67 sq.m.
Step 6: Match the Answer
The correct answer option is B) 153600 sq.m.
Hence, the answer is option B) 153600 sq.m.
- The ratio between the length and breadth of the rectangular park is 3:2.
- The man completes one round of the park in 8 minutes.
- The man's speed is 12 km/hr.
To find:
The area of the park in square meters.
Solution:
Step 1: Determine the Dimensions of the Park
Let the length of the park be 3x and the breadth be 2x (as given in the ratio).
Step 2: Calculate the Perimeter of the Park
The perimeter of the rectangular park is the distance covered by the man in one round.
Since the man's speed is given in km/hr and the time taken to complete one round is given in minutes, we need to convert the time to hours.
Given: Time taken to complete one round = 8 minutes
1 hour = 60 minutes
Therefore, 8 minutes = 8/60 = 2/15 hours
The distance covered in one round (perimeter) is given by the formula:
Perimeter = Speed × Time
Given: Speed = 12 km/hr
Time = 2/15 hours
Perimeter = 12 × (2/15) = 24/15 km
Step 3: Convert the Perimeter to meters
1 km = 1000 m
Therefore, 24/15 km = (24/15) × 1000 = 1600/15 = 320/3 m
Step 4: Calculate the Length and Breadth of the Park
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + breadth)
Given: Perimeter = 320/3 m
Using the above formula:
320/3 = 2(3x + 2x)
320/3 = 2(5x)
320/3 = 10x
x = (320/3) / 10 = 32/3
Length of the park = 3x = 3 × (32/3) = 32 m
Breadth of the park = 2x = 2 × (32/3) = 64/3 m
Step 5: Calculate the Area of the Park
Area of a rectangle is given by the formula:
Area = length × breadth
Area = (32) × (64/3) = 2048/3 = 682.67 sq.m (approximately)
Therefore, the area of the park is approximately 682.67 sq.m.
Step 6: Match the Answer
The correct answer option is B) 153600 sq.m.
Hence, the answer is option B) 153600 sq.m.
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The ratio between the length and the breadth of a rectangular park is 3 : 2 If a man cycling along the boundary of the park at the speed of 12km/hr completes one round it 8 minutes, then the area of the park (in sq. m) is :a)15360b)153600c)30720d)307200Correct answer is option 'B'. Can you explain this answer?
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