[soop]

You have 2 squares 2cm squared. They're right beside each other, flush. The distance between the centre of the squares is currently 2 cm.

Now, by turning each square 45 degrees so that the corners are touching, how far apart are the centres?

it starts like this: | | | and then looks like this <><> (roughly).

[Guest]

You have 2 squares 2cm squared. They're right beside each other, flush. The distance between the centre of the squares is currently 2 cm.

Now, by turning each square 45 degrees so that the corners are touching, how far apart are the centres?

it starts like this: | | | and then looks like this <><> (roughly).

2.828427125 cm

[Guest]

I performed this on a drawing software and entered the dimensions and I got the answer of:

2

you wanted each side to be 2cm but you said 2 cm squared so the side length should be 1.414213562. Calculator never lies!!

[Guest]

I don't think that's right - each side is 2 cm, which makes the centers of the squares two cm apart at the outset. But once you rotate them, you are dealing with the diagonal. So...

Think of it as a triangle, where a right triangle yields the following:

2(squared) + 2 (squared) = (Length of diagonal) squared.

So, that makes it 4+4 = 8 = length of diagonal (squared).

So length of diagonal is sqrt of 8, which is approximately 2.82842712474 - so the first answer was right - because you are traversing 1/2 the diagonal of the first square, then 1/2 the diagonal of the second - a total of one whole diagonal. Make sense?

Edited April 8, 2009 by IdoJava

[Guest]

I don't think that's right - each side is 2 cm, which makes the centers of the squares two cm apart at the outset. But once you rotate them, you are dealing with the diagonal. So...

Think of it as a triangle, where a right triangle yields the following:

2(squared) + 2 (squared) = (Length of diagonal) squared.

So, that makes it 4+4 = 8 = length of diagonal (squared).

So length of diagonal is sqrt of 8, which is approximately 2.82842712474 - so the first answer was right - because you are traversing 1/2 the diagonal of the first square, then 1/2 the diagonal of the second - a total of one whole diagonal. Make sense?

You said it wasn't right but..

the squares were 2cm squared. That's the area.

To find the area you multiply the base times itself(all sides equal). That number that multiplyed by itself is 1.414213562. Therefore each side is that length. Thats how i got my answer.

[Guest]

Granted that the "2 cm squared" may be a little ambiguous, but if the squares are flush next to each other and the distance from one center to the other is 2 cm, then you know it must mean that the squares have 2 cm side lengths.

Rotating the squares means using the diameter of the circumcircle, which is, of course:

2√2

Somehow, this sounds a bit like a geometry homework problem.

[Guest]

You said it wasn't right but..

the squares were 2cm squared. That's the area.

To find the area you multiply the base times itself(all sides equal). That number that multiplyed by itself is 1.414213562. Therefore each side is that length. Thats how i got my answer.

2 squares, aligned and placed right next to eachoter, with 2 cm between their centers... If these 2 squares are the same size, the only possible measures they can have are 2 cm * 2 cm = 4 cm^2 each.

So the wording in the OP must be - at least - unfortunate.

[Guest]

2 squares, aligned and placed right next to eachoter, with 2 cm between their centers... If these 2 squares are the same size, the only possible measures they can have are 2 cm * 2 cm = 4 cm^2 each.

So the wording in the OP must be - at least - unfortunate.

I dont know if he is agreeing with me but they cant have an area of 2 squared and be flush at the same time. I think that is what you're trying to say.

[soop]

2 squares, aligned and placed right next to eachoter, with 2 cm between their centers... If these 2 squares are the same size, the only possible measures they can have are 2 cm * 2 cm = 4 cm^2 each.

So the wording in the OP must be - at least - unfortunate.

Yep, I've done it again. I meant 2cmx 2cm, not 2cm squared.

ok, with the ~2.8 answer, here's another question: If the centre of each square is fixed with a spoke, which in turn is slotted into a 2cm long groove, what angle do both grooves need to be, assuming they are the same angle, in order that the squares can rotate to 45 degree angle.

Imagine the touching bottom corners are hinged, so that they must both rise together.

[Guest]

Yep, I've done it again. I meant 2cmx 2cm, not 2cm squared.

ok, with the ~2.8 answer, here's another question: If the centre of each square is fixed with a spoke, which in turn is slotted into a 2cm long groove, what angle do both grooves need to be, assuming they are the same angle, in order that the squares can rotate to 45 degree angle.

Imagine the touching bottom corners are hinged, so that they must both rise together.

After some quick calculations, I've got 22.5 degrees from the horizontal. I think this is right assuming the groove is a sraight line, but I might be wrong.

[Guest]

By any chance, does anyone here use Autodesk Inventor CAD or any other similar drawing program?

The OP said "flush" and reminded me of Autodesk... and someone else said they used a drawing program to get an answer.

[Guest]

By any chance, does anyone here use Autodesk Inventor CAD or any other similar drawing program?

The OP said "flush" and reminded me of Autodesk... and someone else said they used a drawing program to get an answer.

Yes i did. Unfortunatley it didnt matter because i couldn't solve the problem correctley. I used inventor but you could also use autocad.

[Guest]

You have 2 squares 2cm squared. They're right beside each other, flush. The distance between the centre of the squares is currently 2 cm.

Now, by turning each square 45 degrees so that the corners are touching, how far apart are the centres?

it starts like this: | | | and then looks like this <><> (roughly).

[spoiler='Spoiler for complete workout.

']

The distance between the centres cannot be 2cm when they are placed flush, if the squares are 2cm squared. The measure of a square's area is x*y, or the product of the multiplication of the width and the length/height. Therefore, the distance between the centres would first be the square root of 2 ((1/2 square of 2)times 2), or 1.414cm (rounded to the third decimal).

When the squares are turned by 45 degrees, and the corners are touching, then the square of the long side = the product of the mutliplication of the squares of the two shorter sides, in a triangle with a 90 degree corner, as is a diagonally-cut square. The distance between the centres is then (1/2 ((square root 2 times square root 2) times 2) = 1/2 (2 * 2) = 1/2 (4) = 2cm.

Edited April 8, 2009 by Eternal child

[Guest]

[spoiler='Spoiler for complete workout.

']

The distance between the centres cannot be 2cm when they are placed flush, if the squares are 2cm squared. The measure of a square's are is x*y, or the product the multiplication of the width and the length/height. Therefore, the distance between the centres would first be the square root of 2 ((1/2 square of 2)times 2), or 1.414cm (rounded to the third decimal).

When the squares are turned by 45 degrees, and the corners are touching, then the square of the long side = the product of the mutliplication of the squares of the two shorter sides, in a triangle with a 90 degree corner, as is a diagonally-cut square. The distance between the centres is then (1/2 ((square root 2 times square root 2) times 2) = 1/2 (2 * 2) = 1/2 *4 = 2cm.

We already clarified this. You should read all posts before posting. Don't worry made same mistake before.

[Guest]

We already clarified this. You should read all posts before posting. Don't worry made same mistake before.

Ouch. thanks.

[Guest]

Ouch. thanks.

Sorry, didn't mean to be so harsh. Having a bad day. My bad don't take it personal.

[Guest]

You have 2 squares 2cm squared. They're right beside each other, flush. The distance between the centre of the squares is currently 2 cm.

Now, by turning each square 45 degrees so that the corners are touching, how far apart are the centres?

it starts like this: | | | and then looks like this <><> (roughly).

4 cm?