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eroshea Group Title

Find the number of sides of each of the two polygons if the total number of sides of the polygons is 13, and the sum of the number of diagonals of the polygons is 25.

  • 2 years ago
  • 2 years ago

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  1. hartnn Group Title
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    polygon of n sides have how many diagonals ?

    • 2 years ago
  2. eroshea Group Title
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    [n(n-3)]/2 ... is that it?

    • 2 years ago
  3. hartnn Group Title
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    yes, so u could u form 2 equations using this formula?

    • 2 years ago
  4. eroshea Group Title
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    how?

    • 2 years ago
  5. hartnn Group Title
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    take side of one polygon as x and other as y x+y=13 [x(x-3)]/2+[y(y-3)]/2 = 25

    • 2 years ago
  6. eroshea Group Title
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    after that?

    • 2 years ago
  7. hartnn Group Title
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    can u work out second equation and tell me what u get as x^2+y^2= ?

    • 2 years ago
  8. eroshea Group Title
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    got it :)) the two polygon has 5 and 8 sides

    • 2 years ago
  9. hartnn Group Title
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    yes! that is correct. u had options ?

    • 2 years ago
  10. eroshea Group Title
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    i guess none... im just finding the sides of the two polygons is there a possible option for this problem? if there is, can you tell me what it may be?

    • 2 years ago
  11. hartnn Group Title
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    by option , i meant choices.

    • 2 years ago
  12. eroshea Group Title
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    owh.. hahaha! my bad.. none :)

    • 2 years ago
  13. hartnn Group Title
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    then u worked it out to get 5, 8 ? nice!

    • 2 years ago
  14. eroshea Group Title
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    yes! :)) you helped me a lot there..

    • 2 years ago
  15. pjaesecarilla Group Title
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    hello there :) can i ask @hartnn what you meant by "can u work out second equation and tell me what u get as x^2+y^2= ?" sorry i also encountered this problem on my solid mensuration

    • one year ago
  16. hartnn Group Title
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    so, did u get how i got this : [x(x-3)]/2+[y(y-3)]/2 = 25 ?

    • one year ago
  17. hartnn Group Title
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    when sides is 'x' number of diagonals is x (x-3)/2 same for y and total number of diagonals = 25

    • one year ago
  18. hartnn Group Title
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    that can be simplified as \([x(x-3)]/2+[y(y-3)]/2 = 25 \\ x^2-3x+y^2-3y=50 \\ (x^2+y^2)-3(x+y)=50\) but we know x+y =13 so, \(x^2+y^2-3\times 13=50\) we can easily find x^2+y^2 from here.

    • one year ago
  19. hartnn Group Title
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    and once we know x^2+y^2 and x+y , we can find x and y you know how to ? or need help with that ?

    • one year ago
  20. pjaesecarilla Group Title
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    uhhhh help please :)

    • one year ago
  21. hartnn Group Title
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    ok, so we use the fact that (x+y)^2 = x^2+y^2 +2xy from this we will get xy. right ? then (x-y)^2 = x^2+y^2 -2xy from this we will get x-y , ok ? and now we have x-y, x+y if we just add then, 'y' gets eliminated and you get the value of x try once, if you get stuck, i will show you the entire solution

    • one year ago
  22. pjaesecarilla Group Title
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    ummm is xy=40?

    • one year ago
  23. hartnn Group Title
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    yes ! it is :) xy =40 is correct. what u got for x-y ?

    • one year ago
  24. pjaesecarilla Group Title
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    i kinda got stuck on that one. (x-y)^2 = x^2+y^2-2xy x^2=89-y^2 so. 89-y^2 + y^2 - 2(40) so i got 9. i dunno if im correct :/

    • one year ago
  25. hartnn Group Title
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    see, (x-y)^2 = x^2+y^2 -2xy = 89 -2(40) = 9 so, x-y = 3

    • one year ago
  26. hartnn Group Title
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    x+y = 13 x-y =3 just add them

    • one year ago
  27. pjaesecarilla Group Title
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    OOOOOOOOOOOOHHHHHHHHH!!!!!!! ok thanks man VERY MUCH haha i get it now :))))

    • one year ago
  28. imehs18 Group Title
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    hi pjaesecarilla and hartnn would like to ask about this question. im having problem as well.. how did you get the xy=40

    • one year ago
  29. imehs18 Group Title
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    hi @pjaesecarilla and @hartnn would like to ask about this question. im having problem as well.. how did you get the xy=40

    • one year ago
  30. hartnn Group Title
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    x+y = 13 x^2+y^2 -39 = 50 , so x^2+y^2 = 50+39 = 89 (x+y)^2 = x^2+2xy +y^2 13^2 = 89 + 2xy 169 = 89 +2xy 2xy =169-89 = 80 xy =40 :)

    • one year ago
  31. stephengmt Group Title
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    where did the xy come from? :) pls help thaaaaaaaaanks

    • 4 months ago
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