The length and width of the garden are 93 feet and 62 feet respectively.
Explanation
Suppose, the length of the rectangular garden is [tex]x[/tex] feet.
As the width is exactly two-thirds of the length, so the width of the garden will be: [tex]\frac{2x}{3}[/tex] feet.
310 feet of antique picket fencing are to be used to enclose the garden. It means, the perimeter of the garden is 310 feet.
Formula for perimeter of rectangle [tex]= 2(length+width)[/tex]
So, the equation will be....
[tex]2(x+\frac{2x}{3})= 310\\ \\ x+\frac{2x}{3}= \frac{310}{2}\\ \\ \frac{5x}{3}=155\\ \\ 5x= 465\\ \\ x= \frac{465}{5}=93[/tex]
So, the length of the garden is 93 feet and the width is [tex](\frac{2*93}{3})=62[/tex] feet.
