Question

The number of side of two regular polygon are in the ratio 3 is 252 and their interior angle are in the ratio of 5 is to 3 find the number of their sides

Answer 1

Ratio of sides, n/m = 1/3 -> m = 3n

Ratio of angles, N/M = 3/4 -> M = 4/3N

The interior angle of a regular polygon with n sides is (n-2)*180/n

So we have N = (n-2)*180/n and M = 4/3N = (3n-2)*180/3n

We have two equations and two unknowns.  

We can eliminate N and solve for n, the number of sides:

(n-2)*180/n = (3n-2)*180/4n

n-2 = (3n-2)/4

This gives n = 6

Thus m = 3*6 = 18

So the number of sides are 6 and 18.