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Math Help - scale factor

  1. #1
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    scale factor

    hi, i posted a question a little while ago and it was like this, what are dimensions of an A3 piece of paper is when the A4 piece of paper has been enlarged by scale factor of 2. i got the answer which is 59.4 X 84 cm.

    my question today i like that one so here it is, what is the scale factor of enlargement of an A4 piece of paper ->A5 piece and A3 piece ->A5 piece.

    if anyone can help please post thanks
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  2. #2
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    Quote Originally Posted by andyboy179 View Post
    what is the scale factor of enlargement of an A4 piece of paper ->A5 piece and A3 piece ->A5 piece.
    Study the information (such as the links) provided in this thread.

    Then please reply specifying where you are getting stuck on this exercise.

    Thank you!
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  3. #3
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    Quote Originally Posted by stapel View Post
    Study the information (such as the links) provided in this thread.

    Then please reply specifying where you are getting stuck on this exercise.

    Thank you!
    i just haven't got a clue.
    would the answer for the first one be scale factor 2
    would the answer for the second one be scale factor 2
    im just guessing, now i haven't a clue on any of it really can u HELP please
    thanks
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  4. #4
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    Quote Originally Posted by andyboy179 View Post
    hi, i posted a question a little while ago and it was like this, what are dimensions of an A3 piece of paper is when the A4 piece of paper has been enlarged by scale factor of 2. i got the answer which is 59.4 X 84 cm.

    my question today i like that one so here it is, what is the scale factor of enlargement of an A4 piece of paper ->A5 piece and A3 piece ->A5 piece.

    if anyone can help please post thanks
    The ratio of the width to the height of a sheet of paper is 1:\sqrt2 if that helps?
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  5. #5
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    would A4->A5 = scale factor 2 because 2 A5 pieces of paper are the same as an A4 piece of paper. and A3 -> A5 = scale factor 3 because a A5 piece on its own is 1 of an A3 piece of paper
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  6. #6
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    No, a scale factor of 2 would increase the area by 4 times (2width x 2length = 4area)

    A5 to A4 keeps the width (the smaller measure) the same whereas only the length doubles.
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  7. #7
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    do u know the answer? if so could you please tell me it and explain how you got it .
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  8. #8
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    5You can use the ratio and square it, in this case I am using the shorter side as width and the longer one as length

    For A3 compared to A4

    so the width is 1^2 = 1 (the width doesn't change as you'd expect from putting two sheets of A4 next to each other.

    The length is \sqrt{2}^2 = 2

    Width = 21cm
    Length = 29.7x2 = 59.4cm

    (for the length you can also say 21 \times \sqrt2 \times 2 for a slightly more accurate answer
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  9. #9
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    Quote Originally Posted by stapel View Post
    Study the information (such as the links) provided in this thread.

    Then please reply specifying where you are getting stuck on this exercise.

    Thank you!
    Hey Staple I was hoping if you would just verify what Andy was asking you

    in that thread in the 6th post(The last post)...Was he correct in his

    answer?

    andyboy179 scale factor
    hi, i posted a question a little while ago and it was like this, what are dimensions of an A3 piece of paper is when the A4 piece of paper has been enlarged by scale factor of 2. i got the answer which is 59.4 X 84 cm.

    my question today i like that one so here it is, what is the scale factor of enlargement of an A4 piece of paper ->A5 piece and A3 piece ->A5 piece.

    if anyone can help please post thanks
    First of all make sure that


    • you know that you are dealing with standard dimension.
    • The above point means that An has a fixed size for every n
    • example: A4 will always have dimension 210 x 297 mm
    • 210 mm will be breadth 297 will be length of paper

    Code:
    Observe this table(mm)
    
    A0    841  1189 
      
    A1    594  841   
    
    A2   420  594   
    
    A3   297  420   
    
    A4   210  297   
    
    A5   148  210 
      
    A6   105  148   
    
    A7   74  105   
    
    A8   52  74 
      
    A9   37  52   
    
    A10 26  37
    You will observe from the above that
    • A0 has area 1m^2


    •  Breadth~ of ~A_{n+1} = Length ~of~ A_{n}

    Now what ISO thought while making A size papers

    the area of A0 must be 1 m^2

    it should be a rectangular paper

    so they selected a factor \sqrt{2} between length and breadth

    So if we consider breadth as a , the length will be = a\sqrt{2}

    for A0 computing with area

    a^2 \sqrt{2} = 1m^2

    a^2 = \frac{1}{\sqrt{2}}

    <br />
a= \frac{1}{^4\sqrt{2}}

    a \approx 841mm

    Thus the breadth of A0 = 841 mm , its length = 841\sqrt{2}

    --------------

    Now for A1

    Its breadth = Breadth ~of ~A_0/\sqrt{2}

    Its length = Length~ of ~A_0 /\sqrt{2} ........(this is equal to breadth of A0)

    -------------------
    Thus for any A_{n+1}

    Length = \frac{Length ~of ~A_{n}}{\sqrt{2}}

    Breadth = \frac{Breadth ~of ~A_{n}}{\sqrt{2}}

    Hence the scale factor for respective dimensions of successive members of A series(Like A0 and A1) is \sqrt{2}

    Similarly scale factor for A0 and A2 is \sqrt{2}^2 = 2 ie: both length and breadth differ by a factor of 2

    For A3 to A5 -scale factor is 2

    for A3 to A6 2 \sqrt 2

    your first question wanted you to hypothetically enlarge every size by scale factor 2 all you did was to find new length and breadth if every thing gets hypothetically enlarged by scale factor 2.

    -
    Adarsh
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