Question 182159
John wants to fence a 150 square meters rectangular field. He wants the length and width to be natural numbers {1,2,3,...}. What field dimensions will require the least amount of fencing?
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Max area for a given perimeter is a square, therefore
s = {{{sqrt(150)}}}
s = 12.247 ft
Using natural numbers: square field 12 by 12 (only 48 m of fencing)
But that is only 144 sq/m
:
If you have to have 150 sq/m and the dimensions have to be integers,
15 by 10 would be my answer. This requires 50 m of fencing