Monday, March 3, 2008

PROBLEM OF THE WEEK #22




PQRS is a square. Imagine that it can be folded.

P is folded onto Q.

Then Q. is folded onto R.

If the perimeter of PQRS is 2,

what is the perimeter of the new figure?

40 comments:

Anonymous said...

it should be folded in half and then get your answer 2 divided by 1

Anonymous said...
This comment has been removed by the author.
Daniel Gordon said...

i have no idea, cus how could yiu fold Q onto R? i judt can't vidulize it.

gavriella said...

each side of the square must be .5 and on the new figure the bottom is .5

gavriella said...

daniel try folding a piece of paper to visualize it

Leslie said...

If its .5 on each, then how do you divide it again is it like, .25 or something?

Yardi said...

I agree with gavriella... i folded a piece of paper, P onto Q, then Q to R and it gives you a .5 perimeter.. i THINK

Yacova said...

i agree as well, also its folded into a triagle which is half the perimeter of the square...is that right??

Iris said...

In my opinion, the answer is 1.

Andrew Weatherly said...

If you follow what the directions say it doesn't even make a square so i don't know

Anonymous said...

it is .5 i forgot do the last part of it

Ethan said...

i think it is .5 also because you divide 2 by four because the new shape is a forth of the original square

Danielle said...

so each side starts out as 0.5, and when you follow the directions then each side is 0.25.
...at least thats what i got.

Iris said...

I still think that the answer=1 because in the end each side =.25.
AND .25 multiplied by 4 = 1.

Iris said...

In the 1st folding, the width divides by 2 and in the 2nd folding, the length divides by 2 because PR and QS stay the same way they are during the 1st folding.

Iris said...

So, during the 1st folding, PR + QS are= .5 until the after the 2nd folding.

Anonymous said...

I agree with Ethan Solomon. The new shape is a fourth of the square so you divide it by 4. Then you get .5

Ben S. said...

If the perimeter of PQRS is 2, and PQRS is a square, then at the beginning, each side must be .5. If you fold the square in half, you get a rectangle, .25 by .5
If you fold the rectangle in half along the other axis, you get a square .25 by .25. The perimeter of the figure must then be 1. (.25+.25+.25+.25)

Ben S. said...

and if the perimeter of PQRS is 2, there is no way that each side will be 1... 1+1+1+1 is 4... that is twice what the perimeter should be...


Also, Camellia and Ethan S.- That method would work IF this problem talked about area. Then you would be able to divide the square by 4.

noah said...

folding q on to r would not make it a square because you are folding it diagonally

noah said...

if you fold the side Q S then i agree with ben

Sam said...

Noah, if you fold Q to R after you fold R to S, then you are folding Q to S because R is on top of S.

I think the answer is 1 also because when you fold it the first time you dividethe width by 2. So you have .25 by .5 and the when you fold it agian. so you divide the length by 2. so you have .25 by .25 so then the perimeter is
1(.25+.25+.25+.25)

Anonymous said...

i think once you fold q onto r it makes a square 1 4th of the size of the first square so divide 2 by 8 because there are 4 sides and you fold it 2 times so i believe the answer is 1

Anonymous said...

noah once you fold p onto q r folds onto s to make a rectangle thats y it makes a square

Daniel Gordon said...

i think i get it now, but i'm still not sure about the folding Q onto R.

Allen said...
This comment has been removed by the author.
Allen said...

how is it possible to fold q on r after folding p on q

Jake B said...

i think it is .5 because you take 2 and divide it by two twice

sean said...

i get it its just folding it in half. like when you fold P-Q its also folding R to S
and so on. i got each side being 1/4!

sean said...

i get it its just folding it in half. like when you fold P-Q its also folding R to S
and so on. i got each side being 1/4!

elan said...

wait, each side starts out at .5 and then you fold it and once you do that each side becomes .25?

elan said...

wait, each side starts out at .5 and then you fold it and once you do that each side becomes .25?

Sloan Krakovsky said...

i took a paper adn folded it like the thing said. each side must be .5 becase 2 divided by 4 is .5 and yeah so i think its .5 becaue u just divide the original perimeter by 2 twise

R.J. said...

Isn't it divided by 4 because its in half twice

Rebecca S. said...

I don't really understand the problem, because how can you fold Q to R after folding P to Q?

Rebecca S. said...

I tried folding it with a paper, but it wouldnt fold equally

Rebecca S. said...

I think you could do 2 divided 4 becasue it's folded in half twice.

Mrs. Cooper said...

GREAT!
The perimeter is 1. You are correct in your discussions and observations.

Mitch said...

The answer is .5 because when you fold P to Q you get 1 per side and then when you fold Q to R you get half of one which gives you 0.5

Mrs. Cooper said...

When P is folded onto Q you get a rectangle. When Q is folded onto R you get a square with each side equal to 1/4. So the perimeter is 4(1/4)