Solving Rectangular Park Difference Problem
The problem asks for the difference between the length and breadth of a rectangular park, given their ratio and the park's perimeter.
1. Define Dimensions Using Ratio
Let the length (L) and breadth (B) of the rectangular park be represented based on the given ratio 7:3.
- Let $ L = 7x $
- Let $ B = 3x $
2. Use Perimeter Formula to Find 'x'
The formula for the perimeter (P) of a rectangle is $ P = 2(L + B) $. We are given $ P = 21000 $ m.
- Substitute the expressions for L and B into the perimeter formula: $ 21000 = 2(7x + 3x) $
- Simplify the equation: $ 21000 = 2(10x) $ $ 21000 = 20x $
- Solve for x: $ x = \frac{21000}{20} $ $ x = 1050 $ m
3. Calculate the Difference
The difference between the length and the breadth is $ L - B $.
- Express the difference in terms of x: $ L - B = 7x - 3x = 4x $
- Substitute the value of x found in the previous step: $ \text{Difference} = 4 \times 1050 $ $ \text{Difference} = 4200 $ m
Therefore, the difference between the length and the breadth of the park is 4200 m.
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