Posted on 03/10/2015 5:48:37 PM PDT by MNDude
My daughter has this problem-solving question for her homework. I'm feeling kind of dumb on this one. What do you think is the correct answer?
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
If, as I think has been stated earlier, this is an assignment for a 2nd grader, reasonable people can excuse our objections to the problem.
I used a slide rule.
What you’ve got one of the huge slide rules NASA used for the moonshot? I didn’t know they could do calculations to 19 significant digits. Wow!
(Which is an oblique way of saying I don’t believe your claim to have used a slide rule.)
*no!*, it’s not, it’s 42.
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.
That’s right, you cannot know unless you know the shape.
The minimum length would be if it were square — each side would be the square root of 12, or 2 X square root of 3.
So if each side was 2X sqrt 3, total would be 8X sqrt 3.
Sqrt of 3 is 1.732 -, so you’d need not less than 13.86 inches. Any other dimensions and its longer.
And I don’t believe you are multiplying to 12. So I guess that makes two of us. Or 2.000000000000000000 of us if you prefer.
It is fairly clear and reasonable to assume that they are assuming the quilt is 4x3 (though this is math and that shouldn’t be left out as it is critical to the answer).
The problem is, any sane person trying to make a complete border around it is going to need 14+4 for the corners. The question is posed only in complete units not fractions so we have to use entire complete units for the corners.
That’s 18, which isn’t even a choice.
Who makes a BORDER around something that doesn’t completely contain it? That’s the definition of the word. I suppose it explains why we have so much trouble without our southern border but I digress...
And none of the answers come out properly for a BORDER of the SAME SIZE UNITS which is the most obvious way to work the problem. They did say it was a quilt.
Who writes this garbage?
“How many total units is it across each side?” Is what it should have asked.
I know it’s just a cute problem, but textbooks are supposed to be proofread against these kinds of silly situations and after so many endless revisions of the things over decades and sometimes even hundreds of years you would think something like this would be worded better. Some things about school never change apparently.
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None of the above!
Four times the square root of 12 would give the minimum number for the length of the border, which is 13.856, so 14 is the closest answer of those offered.
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Actually you could do it with less if it were a circle, and a whole lot less if you gave one end a half twist, and sewed the opposing edges together like a moebius strip.
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>> “ 2x6 and 1x12 would be the same” <<
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Try again!
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Yes, we’re completely tossing out shape.
And shape is not unreasonable to consider at all from a practical standpoint. There are ovals to consider, etc. I once received a triangular-shaped pillow as a gift.
Is math not about precision ???
Questions must be formed precisely.
This question simply smells like a lazy teacher or one who has very little clue about math/logic.
Not only that, does the border overlap the existing perimeter or is it sewed onto the existing perimeter edge?
It certainly sounds reasonable that given infinite possibilities there could be some irregular shape out there whose area and perimeter both equal 12 units. It would be interesting to see a mathematical proof one way or the other. It would also be interesting to see if I could follow said proof :-)
I gave you the exact calculation the way one has to do it when computing with irrational numbers and it gave 12, and even justified the steps with things that are taught in all high-school algebra classes. Your belief or lack thereof is irrelevant to the fact of the matter, which is that without specifying a shape for the blanket the problem is ill-posed, even specifying that the blanket is rectangular the problem remains ill-posed unless one also specifies that the side lengths are rational numbers of units (or better for simplicity integer numbers of units).
42
A 1x12 blanket doesn't need a border; it needs more blanket.
No, at least not unless you are going to consider non-planar blankets. If the shape is not specified but we assume it is a planar shape, the minimum perimeter for a region of fixed area is that of a circle of the given area. (This can be proved using a technique called calculus of variations, which is usually only taught in graduate courses, though some top schools will have undergrad courses covering it.) For area 12 square units this gives 2*pi*sqrt(12/pi) which is approximately 12.28.
Only by having the blanket lie on a surface of positive curvature (like the surface of a sphere) could one get the perimeter to be smaller than 2*pi*sqrt(12/pi).
Applying that logic would throw out virtually every story problem in every grade school textbook. It’s an easy problem with an easy solution (at least for an adult), and does a good job of introducing concepts of area and perimeter to a second grader. She can deal with rational and irrational numbers when she’s 18 or 19. And maybe those writers should be more specific. For now, this is a fine problem for a child to solve.
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