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.

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

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Other answers:

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

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