Respuesta :
Answer:
The dimension of the rectangle is;
[tex]18\text{ feet by 8 feet}[/tex]Explanation:
Let l and w represent the length and width of the rectangular garden;
Given;
The width of a rectangular garden is 2 feet more than one third of its length;
[tex]w=\frac{l}{3}+2\text{ -----------1}[/tex]And the perimeter is 52 feet;
The perimeter of a rectangle is;
[tex]\begin{gathered} P=2l+2w=52 \\ 2l+2w=52\text{ ----------2} \end{gathered}[/tex]To get l let us substitute equation 1 to 2;
[tex]\begin{gathered} 2l+2w=52 \\ 2l+2(\frac{l}{3}+2)=52 \\ 2l+\frac{2}{3}l+4=52 \\ 2\frac{2}{3}l=52-4 \\ l=\frac{48}{2\frac{2}{3}} \\ l=18\text{ feet} \end{gathered}[/tex]Using equation 1 we can get the value of w;
[tex]\begin{gathered} w=\frac{l}{3}+2 \\ w=\frac{18}{3}+2 \\ w=6+2 \\ w=8\text{ feet} \end{gathered}[/tex]Therefore, the dimension of the rectangle is;
[tex]18\text{ feet by 8 feet}[/tex]