Question

The length of a rectangular garden is 3.5 less than twice the width. If the perimeter is 65 feet, what is the length of the rectangle?

Answer 1

The length of the rectangle is 20.5 feet.

Explanation:

Let's first translate the expression in the first statement into a mathematical equation:

"The length of a rectangular garden is 3.5 less than twice the width"

if we say length is represented by a variable `l` and width by `w`, we can re-write this as:

`color(purple)(l=2w-3.5)`

We know that the perimeter of any parallelogram (rectangles are included in this) can be written as:

`P=2w+2l=2(w+l)`

Let's substitute the equation for l that we wrote earlier in the equation, and plug in the known perimeter while we're at it:

`65=2(w+color(purple)((2w-3.5)))`

`65=2(3w-3.5)`

`65=6w-7`

`72=6w`

`color(blue)(w=12)`

Now, we know the value of `w`, so let's plug that into our first expression to determine `l`:

`l=2color(blue)((12))-3.5`

`l=24-3.5`

`color(green)(l=20.5)`