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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Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
