Qstnid -B-17- 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. - 16: Understanding Shapes (Including Polygons) Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4

Qstn# B-17 Prvs-Qstn Next-Qstn

#17
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.
Ans : 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˚
∴ ((6n - 4) × 90˚)/((8n - 4) × 90˚) = 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