Solve Polygon Problem: 1:2 Ratio & 3:4 Sum

[1/2"]

polygon problem (?!)

Hi there!
I have got an problem here.It's a simple one.Not much to think about
"The ratio between the numbers of sides of two regular polygons is 1:2 and the ratio between the sum of their 3:4.Find the number of sides in each polygon"
It appears easy and is too. but the problem is the answer i am getting is absolutely weird ie.,
-1 and -2 sides .
In the work out I had considered the no . of sides to be x and 2x
the sum of interior angles 3y and 4y respectively.
so it ends up as {(4x-4)*90} -{(2x-4)*90} =4y-3y
=>180x=y
so i sustituted it in the equation (2x-4)*90=3y which ends up as -4=4x .: x= -1:
Book's answers are polygon with 5 and 10 sides .
I don't know whether I have gone wrong some where. If so Please help me correct it!(If the book's answer is wrong mention that too !)
Thank you

 

[tiny-tim]

Hi 1/2"!

"The ratio between the numbers of sides of two regular polygons is 1:2 and the ratio between the sum of their 3:4.Find the number of sides in each polygon"

If you mean "the ratio between the sum of their interior angles is 3:4", then I agree, the solution is -1 and -2 !

A solution of 5 and 10 would have a ratio of 3:8, not 3:4.

 

[1/2"]

Thanks tiny-tim.