Asked by Rishi

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? PLS ANSWER QUICK!

Answers

Answered by Rishi
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?
Answered by Music Nerd👾
let x be the sides of one polygon
y be the sides of the other polygon

x + y = 13
y = 13 - x

then the formula for the number of polygons is n(n - 3) / 2

x(x - 3) / 2 + y(y - 3) / 2 = 25
x(x - 3) / 2 + ( 13 - x) ( 13 - x - 3) / 2 = 25
x( x - 3 ) / 2 + ( 13 - x) ( 10 - x) / 2 = 25

solve for x
x = 8
y = 13 - 8 = 5



I dunno
Answered by mathhelper
Number of sides of first polygon : x
number of sides in the 2nd = 13-x

number of diagonals of an n-gon = C(n,2) - n = n(n-1)/2 - n
(I subtracted n because the n sides are not diagonals)

number of diagonals for the x-gon
= C(x,2) - x = x(x-1)/2 - x
number of diagonals or the other
= C(13-x, 2) - (13-x) = (13-x)(12-x)/2 - 13 + x

(13-x)(12-x)/2 - 13 + x + x(x-1)/2 - x = 25
multiply and expand at the same time
156 - 25x + x^2 - 26 + 2x + x^2 - x - 2x = 50
2x^2 - 26x + 80 = 0
x^2 - 13x + 40 = 0
(x-5)(x-8) = 0
x = 5 or x = 8

Symmetric solution, that is,
if x = 5, 13-5 = 8
if x = 8, 13-8 = 5

So one is a pentagon, the other an octagon.


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