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JulianMathHelp

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What is the difference between “area” and “shape”? What does it mean when a shape is 5x as large than another shape? Does that mean the area is 5x as large or the dimensions 5x as large?
 
JulianMathHelp said:
What is the difference between “area” and “shape”? What does it mean when a shape is 5x as large than another shape? Does that mean the area is 5x as large or the dimensions 5x as large?
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It means that you are not using clear terminology!

Where did you see someone say "a shape is 5x as large than another shape"? I'm guessing it wasn't a mathematician.
 
This is an excellent question. Sadly, our world does not differentiate very well what it means. It is hoped that mathematics texts and exams are sufficiently clear.

For example, if your cardiologist says your heart is twice the size it should be, does it mean the average radius is twice what it should be? This would be a very serious condition as (2x)^3 = 8x^3 and your heart is EIGHT TIMES the VOLUME it should be. Does it mean the VOLUME is twice what it should be? This is still very bad, but (2x^3)^(1/3) = [2^(1/3)]*x suggests a radius of only 26% greater than it should be - as opposed to 100% greater in the first case.

One must be very careful if one is to understand. Make the speaker or author clarify what is meant by such ambiguous language.

We also hear the VERY ODD statement that something is "5 times smaller" than expected. This is a meaningless statement. It is most likely meant that the size is 1/5 what it should be.

Keep your eyes on this! Too often, someone will use such language deliberately to make their point sound more impressive in some way. Get the facts. Don't believe just the words.
 
Ok, so it’s not good terminology ? Instead, better terminology would be “Figure
A’s sides are 5x as large than another shape’s sides” or “Figure A’s area is 5x as large than another shape’s”? If I were to receive this problem online “How many times large is Figure A than Figure B?”, shall I answer it by sides or area?
 
JulianMathHelp said:
Ok, so it’s not good terminology ? Instead, better terminology would be “Figure
A’s sides are 5x as large than another shape’s sides” or “Figure A’s area is 5x as large than another shape’s”? If I were to receive this problem online “How many times large is Figure A than Figure B?”, shall I answer it by sides or area?
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If we are dealing with planar figures, "how many times larger than" probably refers to area. If it were me, I would write on the exam that I made that assumption.
 
Ok, so the follow up question asks about how many times larger the areas would be, so I'm assuming it's asking about the dimensions because then it's basically asking the same question twice. But yeah, I'll make sure to put my assumption on my paper.
 
JulianMathHelp said:
Ok, so it’s not good terminology ? Instead, better terminology would be “Figure
A’s sides are 5x as large than another shape’s sides” or “Figure A’s area is 5x as large than another shape’s”? If I were to receive this problem online “How many times large is Figure A than Figure B?”, shall I answer it by sides or area?
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I agree with your alternative versions.

But the "how many times as large" question depends on context. In a test about similar figures, I would tend to guess it meant the scale factor, which is the ratio of sides. But if anything in the context suggested a focus on area, my mind would switch over to that.

(Also be careful about whether it says "how many times as large" or "how many times larger"; that verges on idiom, where some people go with what it literally says, while others go with what ordinary people mean by it -- even many textbook authors. What you wrote here, "how many times large", teeters between the two, and is meaningless as written. Your original "5x as large than" was similarly bad English.)

I fully agree with tkhunny's recommendation of stating your assumptions, which is a good idea even when you don't think a problem is at all ambiguous! (Sometimes you just don't see something the same way someone else does, because of your own context.)
 
Ok, so "as large" is different from "larger than" in the sense that if Figure A's sides are 5x larger than Figure B's then Figure A's sides are 6x as large compared to Figure B's sides, and if Figure A's sides are 5x as large compared to Figure B's sides, then, well, they are 5x as large correct? How would you correctly write "5x as large than"? Is it the way I wrote it in this paragraph?
 
Think on what language you might use to describe to objects that are exactly the same size.

"...Once as large..."?
"...One time as large..."?
"...0% larger than..."
 
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