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प्रश्न
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.
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उत्तर
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
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संबंधित प्रश्न
Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
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