Question

If the length L of a rectangle is 3 meters more than twice its width and its perimeter is 300 meters, which of the following equations could be used to find L?

Answer 1

`L="101 m"`
`w = "49 m"`

Explanation:

You have two equations to work with, the equation that describes the perimeter of the rectangle and the equation that describes the relationship between its length, `L`, and width, `w`.

The perimeter of a reactangle is always equal to

`P = 2 *(L + w)`

In your case, you have

`2(L+w) = 300`

Now, you know that if you double the width and add three meters to the result, you get `L`. This means that

`L = 2 * w + 3`

You now have a system of two equations

`{(2L + 2w = 300), (L = 2w + 3) :}`

Use the value of `L` from the second equation to replace `L` in the first equation. This will get you

`L = 2w+3`

`2 * (2w + 3) + 2w = 300`

`4w + 6 + 2w = 300`

`6w = 294 => w= color(green)(49)`

This means that `L` is equal to

`L = 2 * w + 3`

`L = 2 * 49 + 3 = color(green)(101)`

The rectangle will thus be 49 m wide and 101 m long.