Question

Find the number of sides of each of the two polygons if the total number of sides of polygon is 15, and the sum of diagonals of the polygon is 36.

Answer 1

should that be plural...? @miggy9
"and the sum of diagonals of the polygon/s? is 36"

Answer 2

n=number of sides in polygon 1
m=number of sides in polygon 2

number of diagonals in poly 1 = n(n - 3) / 2
number of diagonals in poly 1 = m(m - 3) / 2

now use simultaneous equations to solve from here

Answer 3

n+m = 15
[n(n - 3) / 2] + [m(m - 3) / 2] = 36

Answer 4

n^2-3n/2+m^2-3m/2=36

n^2-3n+m^2-3m/2=72

Then how can I find the value of those two variables?

Answer 5

this eqn is wrong:
n^2-3n+m^2-3m/2=72
should be:
n^2-3n+m^2-3m=72

Answer 6

sorry sorry. the what should be next?

Answer 7

\[\large n^2-3n+m^2-3m=72 =EQN -1\]
\[\large n+m = 15 =EQN -2\]
rearrange equation 2 into the form
m = 15-n
substitute that into EQN 1
solve EQN 1 as now it only has one variable

Answer 8

Thanks.

Answer 9

all good, it's a quadratic so you should get 2 possible answers of M, so pick one and assign the other value to be n, doneski ;)