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.
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.
`(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`
`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.