Question

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

Answer 1

Ratio of sides of two regular polygons = 3 : 4

Let sides of first polygon = 3n

and sides of second polygon = 4n

Sum of interior angles of first polygon

= (2 × 3n - 4) × 90° = (6n - 4) × 90°

and sum of interior angle of second polygon

= (2 × 4n - 4) × 90° = (8n - 4) × 90°

`therefore ((6"n" - 4) xx 90^circ)/(("8n" - 4) xx 90^circ) = 2/3`

`=> ("6n" - 4)/("8n" - 4) = 2/3`

⇒ 18n - 12 = 16n - 8

⇒ 18n - 16n = - 8 + 12

⇒ 2n = 4

⇒ n = 2

∴ No. of sides of first polygon

= 3n = 3 × 2 = 6

and no. of sides of second polygon

= 4n = 4 × 2 = 8