Answer:
• Length=18 inches
,• Width=5 inches
Explanation:
• Let the width of the rectangle = w inches
,•
The length is 2 inches less than 4 times the width.
• Length of the rectangle = (4w-2) inches
,•
We are told that the perimeter of a rectangle = 46 inches.
The perimeter of a Rectangle=2(Length+Width)
Substituting the given values, we have:
[tex]46=2(4w-2+w)[/tex]We solve for w.
[tex]\begin{gathered} 46=2(4w+w-2) \\ \text{Divide both sides by 2} \\ \frac{46}{2}=\frac{2(4w+w-2)}{2} \\ 23=5w-2 \\ \text{Add 2 to both sides} \\ 23+2=5w-2+2 \\ 5w=25 \\ \text{Divide both sides by 2} \\ \frac{5w}{5}=\frac{25}{5} \\ w=5\text{ inches} \end{gathered}[/tex]We then solve for the length.
[tex]\begin{gathered} \text{Length}=4w-2 \\ =4(5)-2 \\ =20-2 \\ =18\text{ inches} \end{gathered}[/tex]The length of the rectangle is 18 inches and the width is 5 inches.
