The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100 , find the length and width of the rectangle. If \( = \) length and \( w= \) width. which of the following systems could be used to solve the problem? \( 1=3 w+2 \) and \( 21+2 w=100 \) \( 1+2=3 w+3 \) and \( 21+2 w=100 \) \( 1+2 w=100 \)

To find the length and width of the rectangle, we start with the given relationship between length and width. Since the length \( l \) is defined as \( 3w + 2 \), we can set up the perimeter equation: \( 2(l + w) = 100 \). Solving this will lead us to the values of \( l \) and \( w \). Now, regarding the system of equations, the first option correctly represents the relationships in this problem. It defines \( l = 3w + 2 \) and accurately uses the perimeter equation \( 2l + 2w = 100 \), which is the appropriate formulation for this scenario! Furthermore, when undertaking the quest for dimensions, double-check that you substitute the expressions properly and manage the perimeter terms carefully—small math errors can lead to wrong conclusions. Remember, sometimes reworking the equations from the start helps illuminate the path to the correct length and width.