anonymous
  • anonymous
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.
Geometry
katieb
  • katieb
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anonymous
  • anonymous
the number of sides is 30
anonymous
  • anonymous
i was able to get the number of sides but i don't know how to show the solution
anonymous
  • anonymous
the number of side is 9 and 6 i just need a solution how to get this

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anonymous
  • anonymous
then the numbers of sides of the polygon should be polygons
kc_kennylau
  • kc_kennylau
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kc_kennylau
  • kc_kennylau
http://www.dummies.com/how-to/content/how-to-find-the-number-of-diagonals-in-a-polygon.html
kc_kennylau
  • kc_kennylau
So the number of diagonals of a polygon with \(n\) sides is \(\dfrac{n(n-3)}2\)
kc_kennylau
  • kc_kennylau
Why don't you set up equations :)
anonymous
  • anonymous
number of diagonals i already given. i need a solution.
anonymous
  • anonymous
can you help me?
kc_kennylau
  • kc_kennylau
You could try letting the numbers of sides of the two polygons be \(m\) and \(n\) respectively :)
anonymous
  • anonymous
can you pls show me the solution. i got this m(m-3)/2 + n(n-3)/2 = 36
kc_kennylau
  • kc_kennylau
Ok I'll set up the equations for you but you'll work out the steps yourself :) \[m+n=15\]\[\frac{m(m+3)}2+\frac{n(n+3)}2=36\]
kc_kennylau
  • kc_kennylau
ok here's a hint: \(m=15-n\)
anonymous
  • anonymous
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
anonymous
  • anonymous
substitute 15-n for m
anonymous
  • anonymous
huh?
kc_kennylau
  • kc_kennylau
substitute \(m=15-n\) to \(\dfrac{m(m-3)}2+\dfrac{n(n-3)}2=36\) :)
kc_kennylau
  • kc_kennylau
into*
anonymous
  • anonymous
\[\left( 15-n ^{} \right)^{2}-3\left( 15-n \right)+n ^{2}-3n=72\]
kc_kennylau
  • kc_kennylau
yep, and this will be a quadratic :)
anonymous
  • anonymous
im stuck
anonymous
  • anonymous
i got -108 = -27n+n^2
kc_kennylau
  • kc_kennylau
Have you learnt quadratic? :)
kc_kennylau
  • kc_kennylau
Use quadratics pl0x
anonymous
  • anonymous
can you just pls provide me the whole solution im stuck. sorry if im stupid about this..
anonymous
  • anonymous
i stop studying for 5years and i need to recall everything about geometry
anonymous
  • anonymous
2n^2-30n+108=0
anonymous
  • anonymous
(_n+_)(_n-_) factor
anonymous
  • anonymous
you did it right you just got 27 instead of 30
anonymous
  • anonymous
how did you get the 30?
anonymous
  • anonymous
got it
anonymous
  • anonymous
from the first equation 225-30n+n^2-45+3n+n^2-3n=72
anonymous
  • anonymous
combine like terms
anonymous
  • anonymous
after that. what is next?
anonymous
  • anonymous
(15-n)^2 gave me the thirty
anonymous
  • anonymous
how do i get the n now?
anonymous
  • anonymous
then you factor the 2n^2-30n+108 you can divide both sides by two to make it easier n^2-15n+54
anonymous
  • anonymous
two factors of 54 that total to -15
anonymous
  • anonymous
(x-_)*(x-_)=0
anonymous
  • anonymous
(n-9)(n-6)
anonymous
  • anonymous
yes so those are your sides
anonymous
  • anonymous
thank you so much for your patience with me. i really appreciate it.

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