In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m². Find the length and breadth of the pond
Solution:
Given, the dimensions of the rectangular lawn is 50m × 40m.
Area of the grass surrounding the pond is 1184 m².
We have to determine the length and breadth of the pond.
Let ABCD be the rectangular lawn and EFGH be the rectangular pond.
Let x m be the width of the grass area around the pond.
So, length of the lawn = 50 m
Breadth of the lawn = 40 m
Length of the pond = (50 - 2x)m
Breadth of the pond = (40 - 2x)m
Area of grass = area of lawn - area of pond
1184 = (50 × 40) - [(50 - 2x) × (40 - 2x)]
1184 = 2000 - [2000 - 100x - 80x + 4x²]
1184 = 2000 - 2000 + 100x + 80x - 4x²
1184 = 180x - 4x²
So, 4x² - 180x + 1184 = 0
Dividing by 4,
x² - 45x + 296 = 0
On factoring,
x² - 37x - 8x + 296 = 0
x(x - 37) - 8(x - 37) = 0
(x - 8)(x - 37) = 0
Now, x - 8 = 0
x = 8
Also, x - 37 = 0
x = 37
When x = 37, the length of the pond = 50 - 2(37) = 50 - 74 = -24
So, x = 37 is not possible.
Therefore, the width of the grass area is 8 m.
Now, length of the pond = 50 - 2(8) = 50 - 16 = 34 m
Breadth of the pond = 40 - 2(8) = 40 - 16 = 24m
Therefore, the length and breadth of the pond is 34 and 24m.
✦ Try This: In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m² [see Fig. 4.1]. Find the length and breadth of the pond
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4
NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 7
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m². Find the length and breadth of the pond
Summary:
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m² [see Fig. 4.1]. The length and breadth of the pond is 34 and 24 m respectively.
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