## 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. 8 months ago 8 months ago

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1. Decart Group Title

the number of sides is 30

2. imehs18 Group Title

i was able to get the number of sides but i don't know how to show the solution

3. imehs18 Group Title

the number of side is 9 and 6 i just need a solution how to get this

4. Decart Group Title

then the numbers of sides of the polygon should be polygons

5. kc_kennylau Group Title

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6. kc_kennylau Group Title
7. kc_kennylau Group Title

So the number of diagonals of a polygon with $$n$$ sides is $$\dfrac{n(n-3)}2$$

8. kc_kennylau Group Title

Why don't you set up equations :)

9. imehs18 Group Title

number of diagonals i already given. i need a solution.

10. imehs18 Group Title

can you help me?

11. kc_kennylau Group Title

You could try letting the numbers of sides of the two polygons be $$m$$ and $$n$$ respectively :)

12. imehs18 Group Title

can you pls show me the solution. i got this m(m-3)/2 + n(n-3)/2 = 36

13. kc_kennylau Group Title

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$

14. kc_kennylau Group Title

ok here's a hint: $$m=15-n$$

15. imehs18 Group Title

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

16. Decart Group Title

substitute 15-n for m

17. imehs18 Group Title

huh?

18. kc_kennylau Group Title

substitute $$m=15-n$$ to $$\dfrac{m(m-3)}2+\dfrac{n(n-3)}2=36$$ :)

19. kc_kennylau Group Title

into*

20. Decart Group Title

$\left( 15-n ^{} \right)^{2}-3\left( 15-n \right)+n ^{2}-3n=72$

21. kc_kennylau Group Title

yep, and this will be a quadratic :)

22. imehs18 Group Title

im stuck

23. imehs18 Group Title

i got -108 = -27n+n^2

24. kc_kennylau Group Title

25. kc_kennylau Group Title

26. imehs18 Group Title

can you just pls provide me the whole solution im stuck. sorry if im stupid about this..

27. imehs18 Group Title

i stop studying for 5years and i need to recall everything about geometry

28. Decart Group Title

2n^2-30n+108=0

29. Decart Group Title

(_n+_)(_n-_) factor

30. Decart Group Title

you did it right you just got 27 instead of 30

31. imehs18 Group Title

how did you get the 30?

32. imehs18 Group Title

got it

33. Decart Group Title

from the first equation 225-30n+n^2-45+3n+n^2-3n=72

34. Decart Group Title

combine like terms

35. imehs18 Group Title

after that. what is next?

36. Decart Group Title

(15-n)^2 gave me the thirty

37. imehs18 Group Title

how do i get the n now?

38. Decart Group Title

then you factor the 2n^2-30n+108 you can divide both sides by two to make it easier n^2-15n+54

39. Decart Group Title

two factors of 54 that total to -15

40. Decart Group Title

(x-_)*(x-_)=0

41. imehs18 Group Title

(n-9)(n-6)

42. Decart Group Title

yes so those are your sides

43. imehs18 Group Title

thank you so much for your patience with me. i really appreciate it.