The length of the rectangle is three times it's width. The perimeter of the rectangle is at most of 112cm. Which inequality models the realationship between the width and the permitted of the rectangle

Let us assume width of the rectangle = w cm.

Length of the rectangle is three times the width.

We took width by w.

Therefore, three times of w = 3*w = 3w.

That is the length of the rectangle.

Perimeter of the rectangle is given by following formula.

Perimeter = 2*length + 2 * width.

We also given that perimeter is at most 112.

Note: "At most" pharse represents less than or equal to.

Therefore, we could setup an inequality as

2*length + 2 * width ≤ 112

Plugging length = 3w and width = w, we get

2*3w + 2*w ≤ 12

or 2w + 2*3w ≤ 12.

Therefore, 2w + 2*3w ≤ 12 inequality models the realationship between the width and the perimeter of the rectangle.