[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.

[mmichaels1970]

Ok. You’ve probably given the best justification for 15. I like your use of “flaps” to help dummies like me visualize. However I still don’t see this as a big indictment of the educational system.

They want the child, for example, to draw this on graph paper. Count -2 boxes inside the quilt and get 12. She may draw up to three quilts if she is really motivated. Then she will count the left side of the border all the way around until she finds a “quilt” that matches one of the given answers.

I just don’t think this is some controversial anti-public education example here.

[The_Reader_David]

But if you gloss “needs” as minimum required without fixing the shape, none of the answers are correct, since she could make a circular blanket and would only need 2*pi*sqrt(12/pi) (approx 12.28) units of border, or if you specify rectangular, but not the dimensions she could get by with a 4*sqrt(12) which is a little less than 14 units.

[The_Reader_David]

Okay, let’s try to save the question:

Baby blankets are rectangular with length to width ratio approximating the golden mean (1+sqrt(5))/2 ). Since A is infeasible, and the length to width ratios needed for a perimeter 15 or perimeter 21 unit blanket are further from the golden mean that that needed for a perimeter 14 blanket, the answer is B.

(Having length to width ratio approximating the golden mean *is* a property baby blankets typically exhibit, while having exact integer length and width in “units”, which should be empirically on the order of a foot is not.)