Question

The length of a rectangle is 4x+3 and the width is 2x-6, how do you write the expression for the perimeter of the rectangle?

Answer 1

`p = 2(4x + 3) + 2(2x - 6)` or simplified `p = 12x - 9`

Explanation:

By definition the perimeter of an object is the length of all its sides.

Also by definition, for a rectangle the 2 sides of the width are equal and the 2 sides of the length are equal.

Therefore the equation for the perimeter of a rectangle can be written as:

`p = 2*l + 2*w` where `p` is the perimeter, `l` is the length and `w` is the width.

Substituting what was given about the length and width gives the equation:

`p = 2(4x + 3) + 2(2x - 6)`

Simplifying this equation gives:

`p = 8x + 3 + 4x - 12`

`p = 8x + 4x + 3 - 12`

`p = 12x - 9`