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eroshea
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.
polygon of n sides have how many diagonals ?
[n(n-3)]/2 ... is that it?
yes, so u could u form 2 equations using this formula?
take side of one polygon as x and other as y x+y=13 [x(x-3)]/2+[y(y-3)]/2 = 25
can u work out second equation and tell me what u get as x^2+y^2= ?
got it :)) the two polygon has 5 and 8 sides
yes! that is correct. u had options ?
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?
by option , i meant choices.
owh.. hahaha! my bad.. none :)
then u worked it out to get 5, 8 ? nice!
yes! :)) you helped me a lot there..
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
so, did u get how i got this : [x(x-3)]/2+[y(y-3)]/2 = 25 ?
when sides is 'x' number of diagonals is x (x-3)/2 same for y and total number of diagonals = 25
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.
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 ?
uhhhh help please :)
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
yes ! it is :) xy =40 is correct. what u got for x-y ?
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 :/
see, (x-y)^2 = x^2+y^2 -2xy = 89 -2(40) = 9 so, x-y = 3
x+y = 13 x-y =3 just add them
OOOOOOOOOOOOHHHHHHHHH!!!!!!! ok thanks man VERY MUCH haha i get it now :))))
hi pjaesecarilla and hartnn would like to ask about this question. im having problem as well.. how did you get the xy=40
hi @pjaesecarilla and @hartnn would like to ask about this question. im having problem as well.. how did you get the xy=40
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 :)
where did the xy come from? :) pls help thaaaaaaaaanks