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The length and the breadth of rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park as an area of 265 m square find the dimensions of the park?
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The length and the breadth of rectangular park are in the ratio of 4 i...
Given information:
- The ratio of length to breadth of the rectangular park is 4:2 or 2:1.
- A 2.5 m wide path runs around the outside of the park.
- The total area of the park and the path combined is 265 m².
Solution:
Step 1: Define Variables
Let the length of the park be 2x and the breadth be x.
Step 2: Calculate the dimensions of the outer rectangle
The outer rectangle formed by the park and the path will have dimensions of (2x + 5) and (x + 5) (adding 2.5 m on each side).
Step 3: Calculate the area of the outer rectangle
The area of the outer rectangle is given by (2x + 5)(x + 5) = 265 m².
Expanding this equation, we get:
2x² + 10x + 5x + 25 = 265
2x² + 15x + 25 = 265
2x² + 15x - 240 = 0
Step 4: Solve the Quadratic Equation
By solving the quadratic equation, we get x = 8 or x = -15. Since dimensions cannot be negative, x = 8.
Step 5: Calculate the dimensions of the park
Therefore, the length of the park is 2x = 16 m and the breadth is x = 8 m.
Step 6: Verify the solution
To verify, calculate the area of the park: 16 * 8 = 128 m².
The area of the path is (2x + 5)(x + 5) - 128 = 265 - 128 = 137 m².
The dimensions of the park are length: 16 m and breadth: 8 m.
- The ratio of length to breadth of the rectangular park is 4:2 or 2:1.
- A 2.5 m wide path runs around the outside of the park.
- The total area of the park and the path combined is 265 m².
Solution:
Step 1: Define Variables
Let the length of the park be 2x and the breadth be x.
Step 2: Calculate the dimensions of the outer rectangle
The outer rectangle formed by the park and the path will have dimensions of (2x + 5) and (x + 5) (adding 2.5 m on each side).
Step 3: Calculate the area of the outer rectangle
The area of the outer rectangle is given by (2x + 5)(x + 5) = 265 m².
Expanding this equation, we get:
2x² + 10x + 5x + 25 = 265
2x² + 15x + 25 = 265
2x² + 15x - 240 = 0
Step 4: Solve the Quadratic Equation
By solving the quadratic equation, we get x = 8 or x = -15. Since dimensions cannot be negative, x = 8.
Step 5: Calculate the dimensions of the park
Therefore, the length of the park is 2x = 16 m and the breadth is x = 8 m.
Step 6: Verify the solution
To verify, calculate the area of the park: 16 * 8 = 128 m².
The area of the path is (2x + 5)(x + 5) - 128 = 265 - 128 = 137 m².
The dimensions of the park are length: 16 m and breadth: 8 m.
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The length and the breadth of rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park as an area of 265 m square find the dimensions of the park?
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The length and the breadth of rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park 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 rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park 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 rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park as an area of 265 m square find the dimensions of the park?.
The length and the breadth of rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park 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 rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park 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 rectangular park are in the ratio of 4 is to 2 or 2.5 m wide pack running or around the outside of the park as an area of 265 m square find the dimensions of the park?.
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