#### Solution:

Given:

- Area of rectangle = `110 cm^2`
- Perimeter of rectangle = `54 cm`
- Length of rectangle = `x`

Since Area = length * width,

`110 = x * "width"`Perimeter = 2(Length + Width)

`110/x = "width"`

`54 = 2(x + 110/x)`

`54 = 2x + 220/x`

`54 = (2x^2 + 220)/x`

`54x = 2x^2 + 220`

`-2x^2 + 54x - 220 = 0`

`-(2x^2 - 54x + 220) = 0`

`2x^2 - 54x + 220 = 0`

`2x^2 - 44x - 10x + 220 = 0`

`2x(x - 22) - 10(x - 22) = 0`

`(x - 22) (2x - 10) = 0`

`x = 22 and 2x = 10`

`x = 22 and x = 5`

Therefore length is 22 and width is `110/22 = 5`

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