Question

(Teaser) The total number of sides in two regular polygons is 13, and total number of diagonals is 25. How many sides are in each polygon?

Answer 1

The other student is correct I believe.

Answer 2

Answer:  

T he two polygons have 8 sides and 5 sides.  

Step-by-step explanation:

A purely algebraic solution seems as if it would be very messy. Use trial and error, along with the formula for the number of diagonals in a n-sided polygon.

number of diagonals in a polygon with n sides: n(n-3)/2

10 sides and 3 sides: 10(7)/2 + 3(0)/2 = 35+0 = 35 nope....

9 sides and 4 sides: 9(6)/2 + 4(1)/2 = 27+2 = 29 nope....

8 sides and 5 sides: 8(5)/2 + 5(2)/2 = 20+5 = 25 yep!