Final answer:
To find the dimensions of Donna's garden, we use the relationship between the width and the length provided, and the perimeter to set up an algebraic equation. After solving, we find that the garden is approximately 2.857 feet in length and 19.142 feet in width.
Step-by-step explanation:
Donna wants to enclose her rectangular garden with a fence. The width of the garden is expressed as 'two more times than three times the length'. We can interpret this as the width being two times the three times the length plus two, or, using algebra, W = 2(3L) + 2. The perimeter (P) is given as 44ft, and since the perimeter of a rectangle is calculated by the formula P = 2L + 2W, we can set up the equation 44 = 2L + 2(2(3L) + 2).
Let's solve for L (length):
44 = 2L + 2(6L + 2)
44 = 2L + 12L + 4
44 = 14L + 4
40 = 14L
L = 40 / 14
L = 20 / 7
L = 2.857 ft (length)
Now, we find W (width):
W = 2(3L) + 2
W = 2(3(2.857)) + 2
W = 2(8.571) + 2
W = 17.142 + 2
W = 19.142 ft (width)
Therefore, the dimensions of Donna's garden are approximately 2.857 feet in length and 19.142 feet in width.