Respuesta :
The perimeter of a rectangle is given by
[tex]p=2l+2w[/tex]Where
p - perimeter
l - length
w - width
We know that the length is 2 inches less than 4 times the width, then
[tex]l=4w-2[/tex]We also know that the perimeter is 86 inches, then
[tex]86=2l+2w[/tex]Now we have two equations:
[tex]\begin{cases}l=4w-2 \\ 86=2l+2w\end{cases}[/tex]Let's just rewrite the equations
[tex]\begin{cases}l-4w=-2 \\ 2l+2w=86\end{cases}[/tex]Now we have a system of equations, let's multiple the first equation by -2
[tex]\begin{cases}-2l+8w=4 \\ 2l+2w=86\end{cases}[/tex]Now we sum the equations
[tex]\begin{gathered} -2l+2l+8w+2w=86+4 \\ \\ 10w=90 \\ \\ w=9\text{ inches} \end{gathered}[/tex]Now we already know that the width is 9 inches. We can find the length using the equation:
[tex]\begin{gathered} l=4w-2 \\ \\ l=4\cdot9-2 \\ \\ l=34\text{ inches} \end{gathered}[/tex]The length is 34 inches and the width is 9 inches.
