Let the length of the rectangle be "l" and width be "w".
The length is 4 times the width, we can write:
[tex]l=4w[/tex]The area is given as 196. We know area of a rectangle is A = lw, where l is length and w is width. Thus, we can write:
[tex]196=lw[/tex]Substituting the first equation into the second, we can solve for w. The process is shown below:
[tex]\begin{gathered} 196=lw \\ 196=(4w)w \\ 196=4w^2 \\ w^2=\frac{196}{4} \\ w^2=49 \\ w=\sqrt[]{49} \\ w=7 \end{gathered}[/tex]Now, using the 1st equation, we can solve for the length, "l". Shown below:
[tex]\begin{gathered} l=4w \\ l=4\times7 \\ l=28 \end{gathered}[/tex]Answer:
Length = 28 inches
Width = 7 inches
