Answer:
17
Step-by-step explanation:
This is a very neat problem -- for teachers.
Let the number of sides = y
The sum of the interior angles is 180*(y - 2)
We are told that this sum equals 9x^2
So far the equation is
(y - 2)*180 = 9x^2 Divide both sides by 9
(y - 2)*20 = x^2 Remove the brackets on the left.
20*y - 40 = x^2
We need another fact. We get that from the statement that x is three greater than the number of sides (y). Therefore y = x - 3
20*(x - 3) - 40 = x^2
20x - 60 - 40 = x^2 Combine like terms on the left
20x - 100 = x^2 Bring the left side to the right side.
0 = x^2 - 20x + 100 You have a quadratic.
a = 1
b = - 20
c = 100
When you solve the quadratic equation, you get
x = 20
Therefore the number of sides is 17.
