scale factor

**andyboy179** · April 18th 2009, 06:19 AM

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

**stapel** · April 18th 2009, 06:59 AM

Originally Posted by andyboy179

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!

**andyboy179** · April 19th 2009, 04:50 AM

Originally Posted by stapel

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

**e^(i*pi)** · April 19th 2009, 05:23 AM

Originally Posted by andyboy179

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?

**andyboy179** · April 19th 2009, 05:29 AM

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
--
4

**e^(i*pi)** · April 19th 2009, 05:47 AM

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.

**andyboy179** · April 19th 2009, 10:00 AM

do u know the answer? if so could you please tell me it and explain how you got it .

**e^(i*pi)** · April 19th 2009, 11:05 AM

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

**ADARSH** · April 20th 2009, 01:56 AM

Originally Posted by stapel

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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