Let the width of the field = w
∵ The length is four times as the width
∵ The width = w
∴ The length = 4w
∵ The length is decreased by 10 feet
∴ The new length = 4w - 10
∵ The width is increased by 2 feet
∴ The new width = w + 2
The new perimeter is 80 feet
∵ The perimeter of the rectangle = 2(length + width)
[tex]\therefore P=2(4w-10+w+2)[/tex]Let us simplify it
[tex]\begin{gathered} P=2(4w+w-10+2) \\ P=2(5w-8) \\ P=2(5w)-2(8) \\ P=10w-16 \end{gathered}[/tex]Now equate it by 80
[tex]10w-16=80[/tex]Add 16 to both sides
[tex]\begin{gathered} 10w-16+16=80+16 \\ 10w=96 \end{gathered}[/tex]Divide both sides by 10
[tex]\begin{gathered} \frac{10w}{10}=\frac{96}{10} \\ w=9.6 \end{gathered}[/tex]The length is 4 times the width
[tex]\begin{gathered} l=4(9.6) \\ l=38.4 \end{gathered}[/tex]The length is 38.4 feet and the width is 9.6 feet
