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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.
 one year ago
 one year ago
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.
 one year ago
 one year ago

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hartnnBest ResponseYou've already chosen the best response.1
polygon of n sides have how many diagonals ?
 one year ago

erosheaBest ResponseYou've already chosen the best response.1
[n(n3)]/2 ... is that it?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yes, so u could u form 2 equations using this formula?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
take side of one polygon as x and other as y x+y=13 [x(x3)]/2+[y(y3)]/2 = 25
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
can u work out second equation and tell me what u get as x^2+y^2= ?
 one year ago

erosheaBest ResponseYou've already chosen the best response.1
got it :)) the two polygon has 5 and 8 sides
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yes! that is correct. u had options ?
 one year ago

erosheaBest ResponseYou've already chosen the best response.1
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?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
by option , i meant choices.
 one year ago

erosheaBest ResponseYou've already chosen the best response.1
owh.. hahaha! my bad.. none :)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
then u worked it out to get 5, 8 ? nice!
 one year ago

erosheaBest ResponseYou've already chosen the best response.1
yes! :)) you helped me a lot there..
 one year ago

pjaesecarillaBest ResponseYou've already chosen the best response.0
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
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
so, did u get how i got this : [x(x3)]/2+[y(y3)]/2 = 25 ?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
when sides is 'x' number of diagonals is x (x3)/2 same for y and total number of diagonals = 25
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
that can be simplified as \([x(x3)]/2+[y(y3)]/2 = 25 \\ x^23x+y^23y=50 \\ (x^2+y^2)3(x+y)=50\) but we know x+y =13 so, \(x^2+y^23\times 13=50\) we can easily find x^2+y^2 from here.
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
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 ?
 5 months ago

pjaesecarillaBest ResponseYou've already chosen the best response.0
uhhhh help please :)
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
ok, so we use the fact that (x+y)^2 = x^2+y^2 +2xy from this we will get xy. right ? then (xy)^2 = x^2+y^2 2xy from this we will get xy , ok ? and now we have xy, 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
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
yes ! it is :) xy =40 is correct. what u got for xy ?
 5 months ago

pjaesecarillaBest ResponseYou've already chosen the best response.0
i kinda got stuck on that one. (xy)^2 = x^2+y^22xy x^2=89y^2 so. 89y^2 + y^2  2(40) so i got 9. i dunno if im correct :/
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
see, (xy)^2 = x^2+y^2 2xy = 89 2(40) = 9 so, xy = 3
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
x+y = 13 xy =3 just add them
 5 months ago

pjaesecarillaBest ResponseYou've already chosen the best response.0
OOOOOOOOOOOOHHHHHHHHH!!!!!!! ok thanks man VERY MUCH haha i get it now :))))
 5 months ago

imehs18Best ResponseYou've already chosen the best response.0
hi pjaesecarilla and hartnn would like to ask about this question. im having problem as well.. how did you get the xy=40
 4 months ago

imehs18Best ResponseYou've already chosen the best response.0
hi @pjaesecarilla and @hartnn would like to ask about this question. im having problem as well.. how did you get the xy=40
 4 months ago

hartnnBest ResponseYou've already chosen the best response.1
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 =16989 = 80 xy =40 :)
 4 months ago
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