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The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre?
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The sides of a rectangular park are in the ratio 4:3 if its area is 17...
Understanding the Problem
To solve the problem, we need to find the length and width of the rectangular park based on the given ratio and area.
Step 1: Determine the Dimensions
- The ratio of the sides is 4:3.
- Let the length be 4x and the width be 3x.
- The area of a rectangle is given by: Area = Length × Width.
Step 2: Set Up the Equation
- Given that the area is 1728 m², we can set up the equation:
4x * 3x = 1728
- This simplifies to:
12x² = 1728
Step 3: Solve for x
- Divide both sides by 12:
x² = 144
- Taking the square root gives us:
x = 12
Step 4: Calculate Length and Width
- Length = 4x = 4 * 12 = 48 m
- Width = 3x = 3 * 12 = 36 m
Step 5: Calculate the Perimeter
- The perimeter (P) of a rectangle is given by: P = 2(Length + Width)
- Substituting the values:
P = 2(48 + 36) = 2 * 84 = 168 m
Step 6: Calculate the Cost of Fencing
- The cost of fencing is Rs 30 per meter.
- Total cost = Perimeter × Cost per meter
- Total cost = 168 * 30 = Rs 5040
Final Answer
The total cost of fencing the rectangular park is Rs 5040.
To solve the problem, we need to find the length and width of the rectangular park based on the given ratio and area.
Step 1: Determine the Dimensions
- The ratio of the sides is 4:3.
- Let the length be 4x and the width be 3x.
- The area of a rectangle is given by: Area = Length × Width.
Step 2: Set Up the Equation
- Given that the area is 1728 m², we can set up the equation:
4x * 3x = 1728
- This simplifies to:
12x² = 1728
Step 3: Solve for x
- Divide both sides by 12:
x² = 144
- Taking the square root gives us:
x = 12
Step 4: Calculate Length and Width
- Length = 4x = 4 * 12 = 48 m
- Width = 3x = 3 * 12 = 36 m
Step 5: Calculate the Perimeter
- The perimeter (P) of a rectangle is given by: P = 2(Length + Width)
- Substituting the values:
P = 2(48 + 36) = 2 * 84 = 168 m
Step 6: Calculate the Cost of Fencing
- The cost of fencing is Rs 30 per meter.
- Total cost = Perimeter × Cost per meter
- Total cost = 168 * 30 = Rs 5040
Final Answer
The total cost of fencing the rectangular park is Rs 5040.
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Question Description
The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre?.
The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a rectangular park are in the ratio 4:3 if its area is 1728 m square find the cost of fencing it at RS 30 per metre?.
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