9.The number of sides of two regular polygons are in the ratio of 3 :2

1.	9.The number of sides of two regular polygons are in the ratio of 3 :2 and their interior angles are in theratio of 5: 3. Find the number of their sides.
Answer» Let sides of 1st polygon=3A,sides of 2nd polygon=2A, but now according to question, we have [(3A-2)×180°/3A]/[(2A-2)×180°/2A] = 5/3, [(3A-2)×2A]/[(2A-2)×3A] = 5/3, (6A-4)/(6A-6) =5/3, 18A-12=30A-30, 30A-18A=-12+30, 12A=18, A=3/2

9.The number of sides of two regular polygons are in the ratio of 3 :2 and their interior angles are in theratio of 5: 3. Find the number of their sides.

Answer»

Let sides of 1st polygon=3A,sides of 2nd polygon=2A,

but now according to question, we have

[(3A-2)×180°/3A]/[(2A-2)×180°/2A] = 5/3,

[(3A-2)×2A]/[(2A-2)×3A] = 5/3,

(6A-4)/(6A-6) =5/3,

18A-12=30A-30,

30A-18A=-12+30,

12A=18,

A=3/2