Question

The ratio of number of sides of two regular polygons is 3:4 and the ratio of measures of their each interior angle is 8:9. What is the sum of the number of diagonals of both the polygons equal to?

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Answer 1

Step-by-step explanation:

The ratio of number of sides of two regular polygons is 3:4 and the ratio of measures of their each interior angle is 8:9. What is the sum of the number of diagonals of both the polygons equal to?

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 = 4n × 2 = 8

Answer 2

Answer:

multiply both sides of this equation by 12 to get: 3 * (3 * n2) = (2 * n2 + 2) * 4. the ratio of n1/n2 is equal to 6/8 which is equal to 3/4. the ratio of s1/s2 is equal to 720/1080 which is equal to 2/3.

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