Question

The length of a given rectangle is six more than twice its width. Write a fully simplified expression to represent its perimeter.

Answer 1

`Perimeter = 12 + 6y`

Explanation:

Represent the length with x and width with y

By analysis, we have:

Length = 6 + 2 times the width.

Mathematically, the expression is:

`x = 6 + 2 * y`

`x = 6 + 2 y`

Required: Determine the perimeter

Perimeter of a rectangle is calculated as:

`Perimeter = 2 * (Length + Width)`

Substitute x for length and y for width

`Perimeter = 2 * (x + y)`

Substitute 6 + 2y for x

`Perimeter = 2 * (6 + 2y + y)`

`Perimeter = 2 * (6 + 3y)`

Open bracket

`Perimeter = 2 * 6 + 2 * 3y`

`Perimeter = 12 + 6y`