Final answer:
The expression that represents the perimeter of Farmer Mike's pasture is 2(L + W). For his rectangular pasture, the calculation uses the lengths of both the width and the length, and by using the perimeter formula, Farmer Mike can determine the total fencing needed.
Step-by-step explanation:
If Farmer Mike wants to build a fence around the perimeter of his pasture, the expression that represents the perimeter is option C) 2(L + W). The perimeter of a rectangle is calculated by adding together the lengths of all four sides. Since the pasture has two pairs of equal sides, namely length (L) and width (W), the formula for the perimeter simplifies to doubling the sum of one length and one width.
For example, if the pasture had a length of 140 feet and a width of 100 feet, the perimeter would be calculated as follows: 2(140 + 100) = 2(240) = 480 feet. This calculation ensures that Farmer Mike will know exactly how much fencing material he will need to enclose his pasture.
It is also important to remember that 2L + 2W and 2(L + W) are equivalent expressions; thus, both A) and C) would technically yield the same numeric result, but in the context of this question, the standardized formula for perimeter is presented as option C).