The length and width of the garden are 93 feet and 62 feet respectively.
<u><em>Explanation</em></u>
Suppose, the length of the rectangular garden is
feet.
As the width is exactly two-thirds of the length, so the width of the garden will be:
feet.
310 feet of antique picket fencing are to be used to enclose the garden. It means, <u>the perimeter of the garden is 310 feet</u>.
<u>Formula for perimeter of rectangle</u>
So, the equation will be....
![2(x+\frac{2x}{3})= 310\\ \\ x+\frac{2x}{3}= \frac{310}{2}\\ \\ \frac{5x}{3}=155\\ \\ 5x= 465\\ \\ x= \frac{465}{5}=93](https://tex.z-dn.net/?f=2%28x%2B%5Cfrac%7B2x%7D%7B3%7D%29%3D%20310%5C%5C%20%5C%5C%20x%2B%5Cfrac%7B2x%7D%7B3%7D%3D%20%5Cfrac%7B310%7D%7B2%7D%5C%5C%20%5C%5C%20%5Cfrac%7B5x%7D%7B3%7D%3D155%5C%5C%20%5C%5C%205x%3D%20465%5C%5C%20%5C%5C%20x%3D%20%5Cfrac%7B465%7D%7B5%7D%3D93)
So, the length of the garden is 93 feet and the width is
feet.