Question

tamara is creating a model of a rectangle. she has 26 inches of yellow ribbon to use for the border of the rectangle. she wants the length, ( l ), to be 3 inches greater than the width, ( w ). which system of equations could tamara use to find the dimensions of a rectangle that uses all of the ribbon?

( \begin{cases} 2l + 2w = 26 \\ 3l = w end{cases} )

( \begin{cases} 2l + 2w = 26 \\ l = 3w end{cases} )

( \begin{cases} 2l + 2w = 26 \\ l = w + 3 end{cases} )

( \begin{cases} 2l + 2w = 26 \\ l + 3 = w end{cases} )

Explanation:

Step1: Set up perimeter equation

The perimeter of a rectangle is $2l + 2w$, and it equals the 26-inch ribbon:
$2l + 2w = 26$

Step2: Relate length and width

Length $l$ is 3 inches greater than width $w$:
$l = w + 3$

Step3: Match to options

Compare the two equations to the given choices.

Answer:

$\boldsymbol{

$$\begin{cases} 2l + 2w = 26 \\ l = w + 3 \end{cases}$$

}$ (the third option)