Answers

2014-01-14T20:56:08+08:00
Let x and y be the two polygons
x + y = 13

the formula for a diagonal in a polygon is  \frac{n(n-3)}{2}
Also since the sum of the diagonals is 25 you can write:

 \frac{x(x-3)}{2} +\frac{y(y-3)}{2} =25
Multiplying both sides by two you get,
x^2 - 3x + y^2 - 3y = 50

Since you can transpose y to the other side you can get: 
x + y = 13 can be written as: x = 13-y

Substituting,
(13-y)^2 - 3(13-y) + y^2 - 3y = 50
169 - 26y + y^2 - 39 + 3y + y^2 - 3y = 50
2y^2 - 26y + 80 = 0
Dividing by two you get,
y^2 - 13y + 40 = 0
(y-5)(y-8) = 0

Therefore the answer can be
1) x = 5, y = 8
OR
2) y=5, x=8
2 4 2