First of all, I consider myself an equal opportunity integer/non-integer type of guy. I have used both of them without reservation for many years.
Alas, but 3.4641016... units per side (approximate square root of 12 actually equals 11.99999999...) will not get you 12 or 12.0 square units. Therefore, I assume you are using “new math” or “common core math”, in which case your solution would be correct.
In new math, 11.999999... is the equivalent of 12.0 because you feel it is so. Feelings really count in new math. One would not want to slight the problem solver by requiring an exact answer that could denigrate their self worth. In fact, 13 or 15 would be appropriate answers if one felt strongly. However, if one felt excessively strong a 12 or 16 answer would also be acceptible.
In common core math, the problem constraint (12.0) would be considered “socially unjust” and could be ignored if desired. The ultimate “right” answer would have to be the answer derived by “group think”. If you could convince the others in the group that 15 was the socially just answer then 15 would be declare the “correct” answer. If other groups came up with different answers, that would be considered OK.
The real problem with these two approaches, although they support social justice and individual freedoms, is that there are flaws when applied in “reality”. Consider a brain surgeon, nuclear physicist, lawyer or judge, etc. who uses that logic in their day to day business. Consider that we have observed this line of thought already in the Supreme Court’s decision on CommieCare.
Me too. I have a BS in mathematics, and a PhD in physics, and use advanced math in my software development projects every day.
Alas, but 3.4641016... units per side (approximate square root of 12 actually equals 11.99999999...) will not get you 12 or 12.0 square units.
Alas, but if you think that the "exact" answers are "correct" you are living in a dream world. In reality, you cannot measure -- let alone cut -- a piece of cloth to more than three significant digits. So the "3x4" piece of cloth is no more a whole number than the 3.464 fails to be.
Therefore, I assume you are using “new math” or “common core math”, in which case your solution would be correct.
Therefore, I assume you don't know what significant digits are, in which case most of what you think you know about real world measurements is wrong. They are discussed elsewhere on this thread. Educate yourself.
In new math, 11.999999... is the equivalent of 12.0 because you feel it is so.
IN ALL MATH 11.999999... means an 11 followed by an infinite number of nines. 11 followed by an infinite number of nines is an abbreviation for:
11 + limitN→∞∑n=1N 9(1/10)n
IN ALL MATH, that limit is 12. Has nothing to do with feelings, new math, common core, or anything else. It is a simple fact of our number system that some numbers have more than 1 infinite decimal expansion. I refer you to any book on elementary analysis [usually called advanced calculus] where this is proved.
Consider a brain surgeon, nuclear physicist, lawyer or judge, etc. who uses that logic in their day to day business.
Any physicist who used 3.4641016 as a measured quantity in anything but the most highly refined measurements would, in fact, be laughed off the planet, and at least one (and probably all of the) referee(s) of his paper would tell him it's 3.46. [Except in quantum electrodynamics, and a few other applications.] The same applies to 3.000000 which is 3.00 in any household measurement you want to discuss. 3.00 x 4.00 does not equal the pure number 12. It equals 12.0: Three significant figures. That's all you get, and that number is the same as 12.05 and 11.95, and arguing about it makes you a pedant, but it doesn't make you right.
Even in pure mathematics, the perimeter of a cloth is not well defined. Perimeters almost invariably have fractional dimensionality and not the linear dimensionality most people learn.
For the seamstress, it might well be 14[.0 ONLY!], but to a bacterium crawling around the edge, it might well be 100 feet [because bacteria have to crawl not straight across the ruler's edge, but up/down/across from fiber to fiber], and to a photon flicking around the perimeter of a charged static cloth from the electrons in one atom to the next, it could be 100 meters.
Contrary to your sentiments, I am not on board with touchyfeely. I think most of our math education in this country is a disaster, and has been so since about 1964, when most of these hideous concepts found their way into the curriculum.
That is exactly why I don't accept the answer of 14. It is false to claim that the answer is 14. The truth is that this is a completely under-specified problem. Even if you assume that the dimensions must be rectangular, there are an infinite number of correct answers to this question, and that is the answer that a person who believes in rigorous mathematics should insist on. [Consult a book on modern algebra in which the general theory of the solutions of linear equations is discussed for details: a system of two equations in three unknowns doesn't have "one" answer. It's rigorously proved. It's what God knows to be true.]
It is a mistake to believe that poorly posed questions have answers. They don't. Because they are not really questions at all.