Maths problem, sheets of paper?

Question

Really battling with figuring this out...

A lot of paper comes in standard sizes A0; A1; A2; A3 etc. A0 can be cut in half to give two sheets of A1; A1 can be cut in half to give two sheets of A2 and so on.

Call the sides of A1 x and y (y being the longest edge)

1. All the pieces of paper are similar. Form an equation involving x and y.

2. Size A0 has an area of 1m^2. Calculate the values of x and y correct to the nearest mm.

3. Hence calculate the length of a sheet of A4.

Thanks in advance :)

Answer 1

I'm not sure there's enough to go on here...

We've got a reference area to work with - 1m^2 - but we have no reference lengths to begin with...

Answer 2

A0=2A1=4A2=8A3=16A4  from the given data.

here the paper is assumed as a rectangle because one edge was bigger than the other

area of A1=1m^2

area of rectangle=y*x  

so area of A1= y*x= 1

y is greater than x

so y-x>0

then y=1/x

i will suggest the values

y=2m, x=0.5m

these values or approximate. i am not sure whether these are correct or not.....

if this information is helpful to you i will be very happy

good luck

Answer 3

What I would do in this case is cheat like so...

Take the measurement of a sheet of standard A4 paper and work back from there by doubling it up at each stage, listing the area of each piece until I'd gained the area of A0 and come to a natural stop.

Another way is divide the known area of A0 by two, do the same to A1 and so on down the line until I'd arrived at A4 which anyone can measure and check that the other calcs are correct.

Another way is to use Sello tape to double an A4 sheet then continue in the same manner to reach the state of an A3,then A2,then A1, and Finally A0, measuring the area of each sheet size as you proceed through each stage you should end up with 1m^2 of paper at A0.

bearing in mind that each piece of this puzzle as you progress should be oblong in shape, hence the Xand Y in the question

All you are doing is halving the area at each division and measuring the long and short side of the paper for a result

you may need to discard some of the surplus sizes ie two A4 make one A3 but you only need the area of one sheet of A4 not two to work toward a formulae

As for the formulae it may dawn on you as you proceed but then it is your homework not ours.