0
$\begingroup$

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

  • 0
    Here it is: http://math.stackexchange.com/questions/2072973/two-squares-of-side-2x-overlap-to-form-a-regular-octagon-how-long-is-each-side – 2017-01-27
  • 0
    i know howeevr, there is no drawing and their answer is unclear. and i cannot comment because i dont have enough reoutations – 2017-01-27
  • 0
    @rohan look above – 2017-01-27
  • 0
    One answer has been deleted which gives more explanation that the existing one. Can I post that?? – 2017-01-27
  • 0
    i dont know its upto u if it helps @rohan – 2017-01-27
  • 0
    All right, excuse me. As you say, it is a question of perspective (btw, the solution by Rohan is nevertheless rather simple). About the title, I am not alone to think that it must contain all **keywords** that indicate the content 1) for catching the interest of people it 2) for retrieval, later on. Very frequently, I find thorough pieces of information by "crossing" two or three keywords. The adjective "tricky", depending so much on the perspective as you say, certainly cannot serve as a keyword. – 2017-01-28
  • 0
    @JeanMarie it is my question i chose what to include. thank u – 2017-01-28

2 Answers 2

1

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

  • 0
    wait what did u jsut do here???? why is ab=sqrt2x and everythign else????? how did u get these numers u should explain – 2017-01-27
  • 0
    @exchangehelpforuni, isn't $ABC$ a right angled triangle? I just used pythagorean theorem. Therefore $AB=\sqrt{2}x$ – 2017-01-27
  • 0
    how did u use pytahgorean theorm if u only know what one side is? – 2017-01-27
  • 0
    nevermind i got it i was being stupid – 2017-01-27
  • 0
    plz calrify how u got ad... i know u did ab-x, but what is the x – 2017-01-27
  • 0
    nevermind i got i just needed to look closer, thank u for the vvvv clear answer – 2017-01-27
3

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:

$2x=2y+z$

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

$y=(z\sqrt{2})/2$

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

Hope it helps.

  • 0
    @rohan thank u v much. however i do not get why z is the hypotenuse... – 2017-01-27