Answers

  • Brainly User
2015-10-13T16:05:50+08:00
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.

( \frac{x(x-3)}{2} )+( \frac{(x-12)(x-15)}{2} ) = 36

x
² - 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
1 5 1