A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border of 2 feet wide surrounding it. If the length of the garden is to be twice the width, what will be the dimensions of the garden? What will be the area of the garden?

Imagine a rectangular area that represents the garden. Then, add a uniform margin of 2 ft around it. So, the length and width dimensions of the bigger outer rectangle would be added with 4 ft each, accounting for two 2-ft marginal distances on both ends. This would be the perimeter:

2 (L+4) + 2 (W+4) = 46

Since L = 2W

2 (2W + 4) + 2 (W+4) = 46

4W + 8 + 2W + 8 = 46

W = 5 ft

L = 2 (5) = 10 ft

Therefore, the dimensions of the garden is 10 ft in length and 5 ft in width. The area, consequently, is calculated as:

A = LW

A = (10 ft) (5 ft)

A = 50 ft²

Thus, the area of the garden is 50 ft².