Answered

IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng mga eksaktong sagot. Ang aming komunidad ay handang magbigay ng malalim at maaasahang mga sagot, anuman ang kahirapan ng iyong mga katanungan.

Find the number of sides of each of the two polygons if the total number of sides of the polygons is 15 and the sum of the number of diagonals is 36

Sagot :

Let x and y be the polygons:
x + y = 15

First Polygon = x
Second Polygon:  15-x
   x + y = 15
   y = 15-x

Number of Diagonals in each polygon = n (n-3)         
                                                                  2
Where n = number of sides of regular polygon  

Number of Diagonals for First Polygon, x:
  = x(x-3)
       2

Number of Diagonals for Second Polygon, 15-x:
   = (15-x) (15-x-3)      or   (x-12)(x-15)            
              2                            2

Add the diagonals of the two polygons.  The sum is 36.

[tex]( \frac{x(x-3)}{2} )+( \frac{(x-12)(x-15)}{2} ) = 36[/tex]

x² - 15x + 90 = 36
x² - 15x + 90-36 = 0
x² - 15x + 54 = 0

Solve by factoring:
(x-9) (x-6) = 0

x - 9=0       x - 6 = 0
x = 9          x = 6

The two polygons have sides of 6 and 9:
Hexagon = 6 sides
Nonagon = 9 sides

To check:
The sum of sides of two polygons is 15
6 + 9 = 15

The diagonals:
Polygon  with 6 sides = 6 (6-3) 
                            2
                     = 6(3) 
                         2
                     = 18/2
                     = 9 diagonals

Polygon with 9 sides = 9 (9-3) 
                                       2
                                  = 9 (6) 
                                       2
                                  = 54/2
                                  = 27 diagonals

The sum of the number of diagonals:
9 + 27 = 36
Maraming salamat sa iyong pakikilahok. Patuloy na magbahagi ng iyong mga ideya at kasagutan. Ang iyong kaalaman ay mahalaga sa ating komunidad. Gawin mong pangunahing mapagkukunan ang IDNStudy.com para sa maasahang mga sagot. Nandito kami para sa iyo.