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The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park?
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The length and the breadth of a rectangular park are in the ratio of 4...
Given:
- The ratio of length to breadth of the rectangular park is 4:2.
- A 2.5 m wide path surrounds the park.
- The area of the path is 265 m square.
To Find:
- Dimensions of the park.
Solution:
Step 1: Determine the dimensions of the park without the path.
Let the length of the park be 4x and the breadth be 2x (since the ratio is 4:2).
The area of the park without the path = length x breadth = 4x * 2x = 8x^2
Step 2: Determine the dimensions of the park with the path.
The length of the park with the path = 4x + 2(2.5) + 2(2.5) = 4x + 5
The breadth of the park with the path = 2x + 2(2.5) + 2(2.5) = 2x + 5
The area of the park with the path = (4x + 5)(2x + 5) = 8x^2 + 20x + 10x + 25 = 8x^2 + 30x + 25
Step 3: Calculate the area of the path.
The area of the path = Area of the park with path - Area of the park without path
265 = 8x^2 + 30x + 25 - 8x^2
265 = 30x + 25
30x = 240
x = 8
Step 4: Find the dimensions of the park.
Length of the park = 4x = 4 * 8 = 32 m
Breadth of the park = 2x = 2 * 8 = 16 m
Therefore, the dimensions of the rectangular park are 32 m x 16 m.
- The ratio of length to breadth of the rectangular park is 4:2.
- A 2.5 m wide path surrounds the park.
- The area of the path is 265 m square.
To Find:
- Dimensions of the park.
Solution:
Step 1: Determine the dimensions of the park without the path.
Let the length of the park be 4x and the breadth be 2x (since the ratio is 4:2).
The area of the park without the path = length x breadth = 4x * 2x = 8x^2
Step 2: Determine the dimensions of the park with the path.
The length of the park with the path = 4x + 2(2.5) + 2(2.5) = 4x + 5
The breadth of the park with the path = 2x + 2(2.5) + 2(2.5) = 2x + 5
The area of the park with the path = (4x + 5)(2x + 5) = 8x^2 + 20x + 10x + 25 = 8x^2 + 30x + 25
Step 3: Calculate the area of the path.
The area of the path = Area of the park with path - Area of the park without path
265 = 8x^2 + 30x + 25 - 8x^2
265 = 30x + 25
30x = 240
x = 8
Step 4: Find the dimensions of the park.
Length of the park = 4x = 4 * 8 = 32 m
Breadth of the park = 2x = 2 * 8 = 16 m
Therefore, the dimensions of the rectangular park are 32 m x 16 m.
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The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park?
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The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park? 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 The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park?.
The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park? 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 The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length and the breadth of a rectangular park are in the ratio of 4:2 . A 2.5 m wide path running all around the outside of the as an area of 265 m square find the dimensions of the park?.
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