(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?

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?

in progress 0
Piper 2 weeks 2021-09-08T07:57:21+00:00 2 Answers 0

Answers ( )

    0
    2021-09-08T07:58:27+00:00

    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!

     

    0
    2021-09-08T07:59:08+00:00

    The other student is correct I believe.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )