SOLUTION: 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?
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Question 1120642: 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?
Found 2 solutions by greenestamps, solver91311:
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!
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!
Answer: the two polygons have 8 sides and 5 sides.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The number of diagonals in a polygon of 
sides is given by }{2})
.
So you have the following information about two polygons, one with sides and one with 
sides. The sum of their sides is 13 and the sum of their diagonals is 25, which is to say:
}{2}\ +\ \frac{m(m\ -\ 3)}{2}\ =\ 25)
Fractions suck, so get rid of them:
\ +\ m(m\ -\ 3)\ =\ 50)
Multiply and collect like terms:
But since 
, we know that 
. So substitute:
^2\ -\ 3(13\ -\ n)\ =\ 50)
Multiply:
Collect like terms in the LHS:
(n\ -\ 8)\ =\ 0)
So 
in which case 
or
in which case 
John
My calculator said it, I believe it, that settles it
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