2 squares of side 2x overlap to form a regular octagon. How long is each side of the octagon? Image of question: http://www.ucl.ac.uk/language-centre/placement-tests/UPC/Maths/images/question14.jpg The hint they gave is: Try again. If the middle piece of each side of the square is y, we get a right-angled triangle all of whose sides can be expressed in terms of x and y. Then apply Pythagoras's Theorem.

may you please explain, I do not get it at all. I saw the question posted already, howevr I cannot comment as i still do not have 50 reputations, also the answer they gave it was ununderstandable. may u plz provide a drawing. thank u

  • $\begingroup$ Here it is: math.stackexchange.com/questions/2072973/… $\endgroup$ – Rohan Jan 27 '17 at 13:35
  • $\begingroup$ i know howeevr, there is no drawing and their answer is unclear. and i cannot comment because i dont have enough reoutations $\endgroup$ – exchangehelpforuni Jan 27 '17 at 13:36
  • $\begingroup$ @rohan look above $\endgroup$ – exchangehelpforuni Jan 27 '17 at 13:37
  • $\begingroup$ One answer has been deleted which gives more explanation that the existing one. Can I post that?? $\endgroup$ – Rohan Jan 27 '17 at 13:37
  • $\begingroup$ i dont know its upto u if it helps @rohan $\endgroup$ – exchangehelpforuni Jan 27 '17 at 13:39

Each side of the octagon is equal to $2x-\sqrt{2}x$. enter image description here

  • $\begingroup$ wait what did u jsut do here???? why is ab=sqrt2x and everythign else????? how did u get these numers u should explain $\endgroup$ – exchangehelpforuni Jan 27 '17 at 15:44
  • $\begingroup$ @exchangehelpforuni, isn't $ABC$ a right angled triangle? I just used pythagorean theorem. Therefore $AB=\sqrt{2}x$ $\endgroup$ – Seyed Jan 27 '17 at 15:53
  • $\begingroup$ how did u use pytahgorean theorm if u only know what one side is? $\endgroup$ – exchangehelpforuni Jan 27 '17 at 15:57
  • $\begingroup$ nevermind i got it i was being stupid $\endgroup$ – exchangehelpforuni Jan 27 '17 at 15:58
  • $\begingroup$ plz calrify how u got ad... i know u did ab-x, but what is the x $\endgroup$ – exchangehelpforuni Jan 27 '17 at 16:00

With the OP's permission:

Reproducing a deleted answer:

Let each side of either square be $2x$. This is divided into two pieces of length $y$ outside the second square and a piece of length $z$ inside the second square. Thus:


At each corner of any square is a right triangle with legs $y, y$ and hypotenuse $z$. Now apply the Pythagorean Theorem:


Now eliminate $y$ and get the relationship between $x$ and $z$. The answer follows directly.

Hope it helps.

  • $\begingroup$ @rohan thank u v much. however i do not get why z is the hypotenuse... $\endgroup$ – exchangehelpforuni Jan 27 '17 at 15:50

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