[The_Reader_David]

Assuming the blanket is rectangular, the answer could be any of the choices except A. The perimeter of a rectangle with fixed area is minimized by a square (a simple Calculus 1 problem shows that) so for a 12 square unit rectangle, the minimum perimeter is 4 times the square root of 12, which is approximately 13.86 units. Any perimeter large than this is possible.

Even allowing a blanket of arbitrary shape, in which case a circle minimizes the perimeter (that takes calculus of variations to prove), in which case the circle has radius the square root of 12/pi and thus circumference (as the perimeter of a circle is called) 2*pi times this, which is approximately 12.28, so again A is the only answer among the choices which impossible for an arbitrarily shaped blanket.

Unless there is something in the problem you didn't tell us it is an ill-posed problem -- which is fine if it was included to make the point that not all practical problems translate into mathematical problems with unique solutions, but is horrible if some nitwit teacher is going to insist that one answer is correct because some dolt of a textbook author posed it and gave "the correct" answer in the answer key.

[mmichaels1970]

Can you do some of that calculus and tell me an L and W that multiply to 12 and a 2L+2W that add to one of the other choices? I’m just looking for one set of numbers and will concede.

[PieterCasparzen]

Assuming the blanket is rectangular, the answer could be any of the choices except A. The perimeter of a rectangle with fixed area is minimized by a square (a simple Calculus 1 problem shows that) so for a 12 square unit rectangle, the minimum perimeter is 4 times the square root of 12, which is approximately 13.86 units. Any perimeter large than this is possible.

Even allowing a blanket of arbitrary shape, in which case a circle minimizes the perimeter (that takes calculus of variations to prove), in which case the circle has radius the square root of 12/pi and thus circumference (as the perimeter of a circle is called) 2*pi times this, which is approximately 12.28, so again A is the only answer among the choices which impossible for an arbitrarily shaped blanket.

Unless there is something in the problem you didn't tell us it is an ill-posed problem -- which is fine if it was included to make the point that not all practical problems translate into mathematical problems with unique solutions, but is horrible if some nitwit teacher is going to insist that one answer is correct because some dolt of a textbook author posed it and gave "the correct" answer in the answer key.

Interesting, the question again was:

Mrs. Feltner wants to put a border on a baby blanket. The area of the blanket is 12 square units. Which shows how many units of materials she needs for the border?

A 12 units B 14 units C 15 units D 21 units

Note the word "needs", as in "Which shows how many units of material she needs..."

While B, C and D would all be sufficient for a 3x4 blanket, B, 14, would be all that was "needed", i.e., the minimum. Although the question does not clarify this by saying which is the "minimum required".

We must also note that 14 units length of border material would result in borders that exactly matched the 3x4 sides of the blanket, if it is 3x4, but would leave the corners borderless; the borders would be like "flaps" at the edges of the blanket, a border with its corners missing.

If we wanted to be that sticky and stay with the assumption that the person wants to know the "minimum" "needed", we could say C) 15 and have a border with corners.

Of course, the question gives no guidance on shape, so as a silly word question for those not really "into" math or logic, B would seem to be the answer that is sought by the teacher.

This question/thread demonstrates a school system that is no place to learn math.