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imehs18 Group Title

Find the number of sides of each of the two polygons if the total numbers of sides of the polygon is 15, and the sum of the number of diagonals is 36.

  • one year ago
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  1. Decart Group Title
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    the number of sides is 30

    • one year ago
  2. imehs18 Group Title
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    i was able to get the number of sides but i don't know how to show the solution

    • one year ago
  3. imehs18 Group Title
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    the number of side is 9 and 6 i just need a solution how to get this

    • one year ago
  4. Decart Group Title
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    then the numbers of sides of the polygon should be polygons

    • one year ago
  5. kc_kennylau Group Title
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    |dw:1384944170133:dw|

    • one year ago
  6. kc_kennylau Group Title
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    http://www.dummies.com/how-to/content/how-to-find-the-number-of-diagonals-in-a-polygon.html

    • one year ago
  7. kc_kennylau Group Title
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    So the number of diagonals of a polygon with \(n\) sides is \(\dfrac{n(n-3)}2\)

    • one year ago
  8. kc_kennylau Group Title
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    Why don't you set up equations :)

    • one year ago
  9. imehs18 Group Title
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    number of diagonals i already given. i need a solution.

    • one year ago
  10. imehs18 Group Title
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    can you help me?

    • one year ago
  11. kc_kennylau Group Title
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    You could try letting the numbers of sides of the two polygons be \(m\) and \(n\) respectively :)

    • one year ago
  12. imehs18 Group Title
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    can you pls show me the solution. i got this m(m-3)/2 + n(n-3)/2 = 36

    • one year ago
  13. kc_kennylau Group Title
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    Ok I'll set up the equations for you but you'll work out the steps yourself :) \[m+n=15\]\[\frac{m(m+3)}2+\frac{n(n+3)}2=36\]

    • one year ago
  14. kc_kennylau Group Title
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    ok here's a hint: \(m=15-n\)

    • one year ago
  15. imehs18 Group Title
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    m^2-3m+n^2-3n = 72 m^2+n^2-3(m+n) = 72 we know that m+n = 15 m^2+n^2-3(15) = 72 m^2+n^2 = 27 after that i dont know

    • one year ago
  16. Decart Group Title
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    substitute 15-n for m

    • one year ago
  17. imehs18 Group Title
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    huh?

    • one year ago
  18. kc_kennylau Group Title
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    substitute \(m=15-n\) to \(\dfrac{m(m-3)}2+\dfrac{n(n-3)}2=36\) :)

    • one year ago
  19. kc_kennylau Group Title
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    into*

    • one year ago
  20. Decart Group Title
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    \[\left( 15-n ^{} \right)^{2}-3\left( 15-n \right)+n ^{2}-3n=72\]

    • one year ago
  21. kc_kennylau Group Title
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    yep, and this will be a quadratic :)

    • one year ago
  22. imehs18 Group Title
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    im stuck

    • one year ago
  23. imehs18 Group Title
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    i got -108 = -27n+n^2

    • one year ago
  24. kc_kennylau Group Title
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    Have you learnt quadratic? :)

    • one year ago
  25. kc_kennylau Group Title
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    Use quadratics pl0x

    • one year ago
  26. imehs18 Group Title
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    can you just pls provide me the whole solution im stuck. sorry if im stupid about this..

    • one year ago
  27. imehs18 Group Title
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    i stop studying for 5years and i need to recall everything about geometry

    • one year ago
  28. Decart Group Title
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    2n^2-30n+108=0

    • one year ago
  29. Decart Group Title
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    (_n+_)(_n-_) factor

    • one year ago
  30. Decart Group Title
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    you did it right you just got 27 instead of 30

    • one year ago
  31. imehs18 Group Title
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    how did you get the 30?

    • one year ago
  32. imehs18 Group Title
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    got it

    • one year ago
  33. Decart Group Title
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    from the first equation 225-30n+n^2-45+3n+n^2-3n=72

    • one year ago
  34. Decart Group Title
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    combine like terms

    • one year ago
  35. imehs18 Group Title
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    after that. what is next?

    • one year ago
  36. Decart Group Title
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    (15-n)^2 gave me the thirty

    • one year ago
  37. imehs18 Group Title
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    how do i get the n now?

    • one year ago
  38. Decart Group Title
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    then you factor the 2n^2-30n+108 you can divide both sides by two to make it easier n^2-15n+54

    • one year ago
  39. Decart Group Title
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    two factors of 54 that total to -15

    • one year ago
  40. Decart Group Title
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    (x-_)*(x-_)=0

    • one year ago
  41. imehs18 Group Title
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    (n-9)(n-6)

    • one year ago
  42. Decart Group Title
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    yes so those are your sides

    • one year ago
  43. imehs18 Group Title
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    thank you so much for your patience with me. i really appreciate it.

    • one year ago
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