Greetings!
Let l represent the length of the rectangle.
Let w represent the width of the rectangle.
[tex] \left \{ {{2(l+w)=46} \atop {3w-1=l}} \right. [/tex]
Isolate for the l in Equation #2.
[tex]3w-1=l[/tex]
[tex]l=3w-1[/tex]
Substitute Equation #2 into Equation #1.
[tex]2(l+w)=46[/tex]
[tex]2[(3w-1)+w)]=46[/tex]
Combine Like Terms.
[tex]2(4w-1)=46[/tex]
Distribute the Parenthesis.
How? Multiply the terms inside the Parenthesis by the term outside of the Parenthesis.
[tex]2*4w-2*1=46[/tex]
[tex]8w-2=46[/tex]
Add 2 to both sides.
[tex](8w-2)+2=(46)+2[/tex]
[tex]8w=48[/tex]
Divide both sides by 8.
[tex] \frac{8w}{8}= \frac{48}{8} [/tex]
[tex]w=6[/tex]
The Answer Is:
[tex] \left[\begin{array}{ccc}w=6\end{array}\right] [/tex]
The Width is 6 units and the Length is 17 units.
Hope this helps.
-Benjamin
