# The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width with the same...

The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width with the same area as the flower bed. Calculate the width of the path.

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### 1 Answer

The dimensions of the flower bed is 9m by 6m.

If the constant width is x, then the length of the out rectangle is 9+2x and width is 6+2x.

The area of flower bed `= 9 xx 6 = 54`

The area of the path is same as the flower bed.

Therefore,

`(9+2x)xx(6+2x) - 54 = 54`

`(9+2x) xx (6+2x) = 108`

`54+18x+12x+4x^2 = 108`

`4x^2+30x-54 = 0`

`2x^2+15x-27 = 0`

This gives,

`x = 1.5` or `x = -9`

We know x cannot be negative, therefore `x =1.5.`

**The width of the path is 1.5 m.**