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

A square is a four sided polygon with all the sides equal to each other and every angle being a right angle

A rectangle is a four sided polygon with opposite sides equal to each other and every angle being a right angle

## Answer: The dimension of the square lawn which is bounded on the three sides by a path of 4m wide with area of the path being 7/8 that of the lawn is 16m

Let's find the dimensions of the lawn.

**Explanation:**

Let's draw the figure of the lawn along with the path as shown below

Let the length of the side of the square be 'x'

Area of lawn = x² (Since, area of a square = side^{2})

Length of the outer rectangle = length of the square lawn + 2 × width of the path

= x + 4 + 4 = x + 8

Breadth of the outer rectangle = length of the square lawn + width of the path

= x + 4

Area of the outer rectangle = (x + 4)(x + 8) (Since, area of a rectangle = length × breadth)

= x^{2} + 12x + 32

Area of the path = Area of the outer rectangle - Area of the square

= x^{2} + 12x + 32 - x^{2} (By substituting the values)

= 12x + 32

Area of the path = 7/8 that of the area of the lawn (given)

=> 12x + 32 = (7/8)x²

On solving,

96x + 256 = 7x²

7x² – 96x – 256 = 0

By splitting the middle term we get,

7x² - 112x + 16x - 256 = 0

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

x - 16 = 0 or 7x + 16 = 0

x = 16 or x = -16/7

Since, dimension cannot be negative hence, x = 16 m

### Hence, the dimension of the square lawn which is bounded on the three sides by a path of 4m wide with area of the path being 7/8 that of the lawn is 16m.

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