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A Square Lawn is Bounded on Three Sides by a Path 4 M Wide. If the Area of the Path is 7/8 that of the Lawn, Find the Dimensions of the Lawn. - ICSE Class 10 - Mathematics

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Question

A square lawn is bounded on three sides by a path 4 m wide. If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn.

Solution

Let the side of the square lawn be x m.
Area of the square lawn = x2 m2
The square lawn is bounded on three sides by a path which is 4 m wide.

Area of outer rectangle = (x + 4) (x + 8) = x2 + 12x + 32
Area of path = x2 + 12x + 32 – x2 = 12x + 32
From the given information, we have:

`12x + 32 = 7/8 x^2`

`96x + 256 = 7x^2`

`7x^2 - 96x - 256 = 0`

`7x^2 - 112x + 16x - 256 = 0`

7x(x - 16) + 16(x - 16) = 0

(x - 16)(7x + 16) = 0

`x = 16, (-16)/7`

Since, x cannot be negative. So, x = 16 m.
Thus, each side of the square lawn is 16 m.

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 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6B | Q: 12
Solution A Square Lawn is Bounded on Three Sides by a Path 4 M Wide. If the Area of the Path is 7/8 that of the Lawn, Find the Dimensions of the Lawn. Concept: Quadratic Equations.
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