Answer :
Consider that the area (A) and perimeter (P) of a rectangle with length (L) and width (W) is given by the formulae,
[tex]\begin{gathered} A=L\cdot W \\ P=2\cdot(L+W) \end{gathered}[/tex]Given that the perimeter of the rectangular garden 240 ft,
[tex]\begin{gathered} P=240 \\ 2\cdot(L+W)=240 \\ L+W=120\ldots\ldots(1) \end{gathered}[/tex]Also, it is given that the length is twice the width,
[tex]L=2W[/tex]Substitute this in equation (1) and simplify,
[tex]\begin{gathered} 2W+W=120 \\ 3W=120 \\ W=40 \end{gathered}[/tex]Then the corresponding length will be,
[tex]\begin{gathered} L=2(40) \\ L=80 \end{gathered}[/tex]Now that the length and width of the rectangular garden is known, the area can be calculated as,
[tex]\begin{gathered} A=80\cdot40 \\ A=3200 \end{gathered}[/tex]Thus, the length, width, and area of the rectangular garden are 80 feet, 40 feet, and 3200 square feet, respectively.