Braingle: 'Area of a Square' Brain Teaser

Area of a Square

Math brain teasers require computations to solve.

Puzzle ID:	#4840
Fun:	(2.84)
Difficulty:	(1.76)
Category:	Math
Submitted By:	andy1608
Corrected By:	javaguru

You have a piece of paper, 10cm by 10cm. Area = 100cm^2. For some reason, you need a square piece of paper with an area of 50cm^2. Using the paper you have, what's an easy way of getting the new square?

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Comments

Smart Jun 28, 2002	It's a really good teaser! But it's hard for me. Sort of! But it's great!
sk8babe Jul 17, 2002	You could also just fold the 100x100 square it in half and then half the other way to give a 50x50 square. Gd answr though!! I would never have thought about doing it like that! =¬)
andy1608 Jul 17, 2002	If you fold it in half, then half again to make a square, it's 5cm * 5cm = area 25cm^2, so it doesn't fit the answer.
Deucex2 Jul 22, 2002	Brilliant. Absolutely, completely, snark-farking brilliant. I love it.
deanlilja Jul 22, 2002	Who writes these questions so poorly? Here's another mis-worded one. First you want a 50cm^2 area, and then you want a square. Other problems or riddles here lack sufficient information allowing multiple correct answers. Straingle, not Braingle!
deanlilja Jul 22, 2002	Also, what's with this time-out feature that lets me ponder a teaser for only a minute and then I have to refresh my e-mail to get to the site for answers? What's the point?
andy1608 Jul 22, 2002	you're right, it should have been worded better, stating the paper had to remain a square earlier, thanks for pointing it out.
lizard450 Jul 22, 2002	I understand english and thought the riddle was too hard
lizard450 Jul 22, 2002	I understand english and thought the riddle was too easy i mean... i don't know how you thought it was hard.. i said rip it into 1/4s though
zangel3000 Jul 29, 2002	I'm not trying 2 b meen or anything, but personally, i thought that it was a little dumb.
zangel3000 Jul 29, 2002	I'm not trying 2 b meen or anything, but personally, i thought that it was a little dumb.
dumbell Aug 20, 2002	the question stated that the solution had to be a square.Does it matter where in the question it said so? I liked this one. For deanlilja, I ponder questions for ages with no problems. I suggest the problem could be with your pc or modem. do you have a short idle setting?
Yogi Jul 22, 2003	I had no idea that you cound fold the corners of the square like that and end up with sides of 7.0710678118654752440084436210485 cm each.
willymapo Jul 22, 2003	Hey, The teaser is pretty neat, and the idea was everybody saying "Dumb, it is easy, just folded half and half" later to find out that that will yield to a 25 square. Great teaser.
Monique114 Jul 22, 2003	Great teaser!
krle Jul 26, 2003	There is another way to do so (not that smarts though). Simple math shows that diagonal of the new square is 10cm long. So fold original square so that its diagonal is aligned with one of its 10cm long sides. This corner will show the end of the new 10cm long diagonal. Now it’s easy to make new square.
Bobbrt Jul 29, 2003	I'm not sure why there's so much confusion on this teaser. Seems pretty obvious to me that you need to make a square of 50 cm^2.
something Nov 07, 2004	Very nice. It was so simple, but I couldn't get it. Awesome.
Punk_Rocker Nov 07, 2004	I was gonna say cut it
happymonkey13 Nov 07, 2004	It is really wierd!! i didn't get it!! I don't think it's that great!
Kollonel_Rabbit Jan 11, 2005	WHY NOT JUST FOLD IN HALF 10X10 10/2=5 5X10 = 50 OTHER SIDE STAYS THE SAME
DarkMessiah Feb 29, 2008	you can just fold it in half...........
Jimbo May 06, 2009	Has this teaser been edited? Do some people not understand the word square? I don't really think the given solution provides a single piece of square paper. I agree with the principal but my solution was to join all 4 midpoints of the original square and cut off the triangular corners formed. (Very handy bit of knowledge is that the length of the diagonal in any square is root 2 times the length of the side.) Good puzzle
averageguy May 19, 2011	gosh!!, I can't believe that I actually got it right, I did some algebra first and found out that the length of one side of a square whose area is 50 cm^2 should be 5 square root of 2, I immediately knew that this was half the length of the original square's diagonal, and then, I put another diagonal for each of the four "quadrants" of the square and saw that it was the simply same length as half of the original square's diagonal, the next events were accidental, I didn't even know that I was already forming a square!!! THIS PUZZLE IS COOL!!!