Question

Write an equation that represents the perimeter of the rectangle. The width of a rectangle is 9 less than one-third it's width, when the perimeter is 45.

Answer 1

The equation that represents the perimeter of the rectangle is:

`\text{Perimeter} = (2)/(3) * [4l-27]`

Explanation:

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × [l + w]

It is provided that the width of a rectangle is 9 less than one-third it's length.

That is:

`w = (1)/(3)l-9`

The perimeter is given as 45.

The equation that represents the perimeter of the rectangle is:

`\text{Perimeter} = 2 * [l + (1)/(3)l-9]\\\\\text{Perimeter} = 2 * [(3l+l-27)/(3)]\\\\\text{Perimeter} = 2 * [(4l-27)/(3)]\\\\\text{Perimeter} = (2)/(3) * [4l-27]`

Thus, the equation that represents the perimeter of the rectangle is:

`\text{Perimeter} = (2)/(3) * [4l-27]`