SOLUTION: 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 is 25.

Algebra ->  Polygons -> SOLUTION: 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 is 25.      Log On


   

Question 1009832: 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 is 25.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= number of sides of one of the two polygons
y= number of sides of the other polygons
Since it does not matter which is the one and which is the other, we will find two solutions for x , and the same two solutions for y .
x%2By=13 , because "the total number of sides of the polygons is 13".
The number of diagonals of a polygon with n sides is %28n-3%29%2An%2F2 ,
so "the sum of the number of diagonals is 25" translates as
%28x-3%29%2Ax%2F2%2B%28y-3%29%2Ay%2F2=25<-->%28x-3%29%2Ax%2B%28y-3%29%2Ay=50 .
So, we have
system%28x%2By=13%2C%28x-3%29%2Ax%2B%28y-3%29%2Ay=50%29 .
x%2By=13-->y=13-x
Substituting into %28x-3%29%2Ax%2B%28y-3%29%2Ay=50 , we get
%28x-3%29%2Ax%2B%2813-x-3%29%2813-x%29=50
x%5E2-3x%2B%2810-x%29%2813-x%29=50
x%5E2-3x%2B130-10x-13x%2Bx%5E2=50
2x%5E2-26x%2B130=50
2x%5E2-26x%2B80=0
x%5E2-13x%2B40=0
%28x-8%29%28x-5%29=0-->system%28x=8%2C%22or%22%2Cx=5%29 .
Those are the two solutions.
If x=5 , y=13-x=8 .
If x=8 , y=13-8=5 .
One polygon has highlight%285%29 sides, and the other one has highlight%288%29 sides.