I believe the quickest way to the solution is to utilize the answer choices. This is definitely one of those questions put up to expand one’s mind and to give it a good exercise.
15 cows each need 30 square feet of area ——-> 450 square feet of area
Since the length and width must be integers, we are looking for a factor pair that multiplies to 450.
Concept: given a constant product (here length * width = 450), we minimize the addition of those two numbers by making them as close to equal as possible.
Since all the answer choices are relatively small (we don’t have any sums in the ballpark of 1 + 1 + 450 = 452), it would make sense to start at the factor pair closest to the square root of 450 and work backwards.
Key point: we only have 3 sides of fence. Thus, we will be adding one part of the factor pair twice and the other part of the factor pair once.
18 * 25 = 450
18 + 18 + 25 = 61 (not an answer)
Or
18 + 25 + 25 = 68 (not an answer)
15 * 30 = 450
15 + 15 + 30 = 60 (not an answer)
Or
15 + 30 + 30 = 75 (not an answer)
10 * 45 = 450
10 + 10 + 45 = 65 —— BINGO
Answer *D*
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