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A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.
- a)Rs. 15000
- b)Rs. 15594
- c)Rs. 15500
- d)None of these
Correct answer is 'B'. Can you explain this answer?
Verified Answer
A rectangular garden is 65 cm long and 50 cm wide. Two cross paths eac...
The rectangular field is in m and not in cms .
One Path have measurements 65cm and 2cm and its area is 65*2=130m2.
Area of the other path is 50*2=100m2. Total area of the path=130+100=230m2.
Now since the middle square has been counted two times so we will subtract it So, total area to be constructed =230-2*2 =230-4= 226m2.
So Total Cost=226*69=Rs. 15594
One Path have measurements 65cm and 2cm and its area is 65*2=130m2.
Area of the other path is 50*2=100m2. Total area of the path=130+100=230m2.
Now since the middle square has been counted two times so we will subtract it So, total area to be constructed =230-2*2 =230-4= 226m2.
So Total Cost=226*69=Rs. 15594
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A rectangular garden is 65 cm long and 50 cm wide. Two cross paths eac...
Problem Analysis
We are given the dimensions of a rectangular garden and we have to construct two cross paths parallel to the sides passing through the center of the garden. We are also given the width of the paths and the cost of constructing them per square meter. We have to find the total cost of constructing the paths.
Given Data
Length of the garden = 65 cm
Width of the garden = 50 cm
Width of each path = 2 m
Cost of construction = Rs. 69 per m^2
Solution
1. Convert the given dimensions to meters.
Length of the garden = 65 cm = 0.65 m
Width of the garden = 50 cm = 0.5 m
Width of each path = 2 m
2. Draw a diagram of the garden and the paths to visualize the problem.
3. Since the paths pass through the center of the garden, each path will have a length of the diagonal of the rectangular garden.
Length of the diagonal of the garden = √(65^2 + 50^2) m = 81.55 m
4. The area of each path can be calculated as follows:
Area of each path = Length × Width
Length of each path = Length of the diagonal of the garden = 81.55 m
Width of each path = Width of the garden + Width of the paths on both sides = 0.5 m + 2 m + 2 m = 4.5 m
Area of each path = 81.55 m × 4.5 m = 366.975 m^2
5. The total area of both paths can be calculated as follows:
Total area of both paths = 2 × Area of each path
Total area of both paths = 2 × 366.975 m^2 = 733.95 m^2
6. The total cost of constructing the paths can be calculated as follows:
Total cost = Total area × Cost per square meter
Total cost = 733.95 m^2 × Rs. 69/m^2 = Rs. 50,594.55
Answer
The total cost of constructing the paths is Rs. 50,594.55
Hence, the correct option is (b) Rs. 15,594.
We are given the dimensions of a rectangular garden and we have to construct two cross paths parallel to the sides passing through the center of the garden. We are also given the width of the paths and the cost of constructing them per square meter. We have to find the total cost of constructing the paths.
Given Data
Length of the garden = 65 cm
Width of the garden = 50 cm
Width of each path = 2 m
Cost of construction = Rs. 69 per m^2
Solution
1. Convert the given dimensions to meters.
Length of the garden = 65 cm = 0.65 m
Width of the garden = 50 cm = 0.5 m
Width of each path = 2 m
2. Draw a diagram of the garden and the paths to visualize the problem.
3. Since the paths pass through the center of the garden, each path will have a length of the diagonal of the rectangular garden.
Length of the diagonal of the garden = √(65^2 + 50^2) m = 81.55 m
4. The area of each path can be calculated as follows:
Area of each path = Length × Width
Length of each path = Length of the diagonal of the garden = 81.55 m
Width of each path = Width of the garden + Width of the paths on both sides = 0.5 m + 2 m + 2 m = 4.5 m
Area of each path = 81.55 m × 4.5 m = 366.975 m^2
5. The total area of both paths can be calculated as follows:
Total area of both paths = 2 × Area of each path
Total area of both paths = 2 × 366.975 m^2 = 733.95 m^2
6. The total cost of constructing the paths can be calculated as follows:
Total cost = Total area × Cost per square meter
Total cost = 733.95 m^2 × Rs. 69/m^2 = Rs. 50,594.55
Answer
The total cost of constructing the paths is Rs. 50,594.55
Hence, the correct option is (b) Rs. 15,594.
Community Answer
A rectangular garden is 65 cm long and 50 cm wide. Two cross paths eac...
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A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is 'B'. Can you explain this answer?
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A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is '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 garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is '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 garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is 'B'. Can you explain this answer?.
A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is '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 garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is '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 garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is 'B'. Can you explain this answer?.
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A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is 'B'. Can you explain this answer?, a detailed solution for A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is 'B'. Can you explain this answer? has been provided alongside types of A rectangular garden is 65 cm long and 50 cm wide. Two cross paths each 2 m wide are to be constructed parallel to the sides. If these paths pass through the centre of the garden, find the cost of constructing the paths at the rate Rs. 69 per m2.a)Rs. 15000b)Rs. 15594c)Rs. 15500d)None of theseCorrect answer is 'B'. Can you explain this answer? theory, EduRev gives you an
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