Final answer:
The area (A) of the rectangular garden in terms of the length (l) can be expressed as A = 35l - l², based on the total amount of fencing available which is 70 meters.
Step-by-step explanation:
To calculate the area of a rectangular garden using a given amount of fencing, we need to consider the relationship between the perimeter of the rectangle and its area. The farmer has 70 meters of fencing, which represents the total perimeter (P) of the rectangle. The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle.
Since the farmer's total perimeter is 70 meters, we have the equation 70 = 2l + 2w. We can express the width w in terms of the length l using this equation: w = (70 - 2l) / 2. Now the area (A) of the rectangle, which is l times w, can be expressed in terms of the length l as A = l × w = l × ((70 - 2l) / 2). Simplifying, we get A = 35l - l². Thus, the formula expressing the area (A) in terms of the length (l) of the garden is A = 35l - l².