Answered

IDNStudy.com, kung saan nagtatagpo ang mga tanong at sagot. Ang aming komunidad ay nagbibigay ng eksaktong sagot upang matulungan kang maunawaan at malutas ang anumang problema.

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
Pinahahalagahan namin ang bawat tanong at sagot na iyong ibinabahagi. Patuloy na magbahagi ng impormasyon at karanasan. Ang iyong kaalaman ay mahalaga sa ating komunidad. Para sa mabilis at eksaktong mga solusyon, isipin ang IDNStudy.com. Salamat sa iyong pagbisita at sa muling pagkikita.