# 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

1
by Jbeatrice

• 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.

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