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The corners of the square, 2m. sides, are cut off to form a regular octagon. What is the length of the side of the resulting octagon?

  • geometry - ,

    draw the top part of the cut-off
    let each side of the octagon be x m
    let the amount that has to be cut off be y
    I see a right-angled triangle with hypotenuse x and the other 2 sides are y
    x^2 = y^2 + y^2
    x^2 = 2y^2
    x = 2√y or y = x/√2

    now along the top of the original square:
    y + x + y = 2
    x/√2 + x + x/√2 = 2
    times √2
    x + √2x + x = 2√2
    x(√2+2) = 2√2
    x = 2√2/(√2+2)
    x= 2√2/(√2+2) * (√2-2)/(√2-2)
    = 2√2 - 2 or appr 0.8284

  • LIAN!!! - geometry - ,

    I just noticed that you posted this same question 9 times !
    and it had already been answered.
    Very annoying.

    Don't you check back to see if somebody answered your earlier question??

  • geometry - ,

    i didn't know i posted it 9 times. i always check back the page if my question is answered. hahaha. i keep on refreshing it. lol. THANK YOU SO MUCH!!

  • geometry - ,

    Hmmm. A good lesson. We have been attributing to malice what was done in ignorance.

    So, Lian, once the question is posted, go back to the main list, and click in your link. Then you can refresh the page without reposting the question.

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