Question

The ratio of the sides of two regular polygons is 1 : 2 and their interior angles are in the ratio 3:4,
then the number of sides in each polygon is
(A) 6 12
(B) 5, 10
(0) 12.6
(D) 10.5​

Answer 1

Answer:

take the numbers as 1x 2x and 3x and 4x

Answer 2

The ratio of the sides of two polygon is 1 : 2.
⇒ Let the polygon A have n sides & polygon B have 2n sides.
⇒ The sum of the interior angles of A is (n - 2)×180
∘
= 180
∘
n - 360
∘

⇒ So each interior angle,
⇒
n
180
∘
n−360
∘

​
--- (1)
⇒ Sum of interior angles of B is (2n - 2)×180
∘
= 360
∘
n - 360
∘
.
⇒
2n
360
∘
n−360
∘

​
--- (2)
⇒ Now the ratio of the interior angles of A and B.
⇒
n
180
∘
n−360
∘

​
:
2n
360n
∘
−360
∘

​
::
4
3
​
---- [From (1) and (2)]

⇒
360
∘
n−360
∘

360
∘
n−720
∘

​
=
4
3
​


⇒
360
∘
n(n−1)
360
∘
(n−2)
​
=
4
3
​


⇒ 4n−8=3n−3

∴ n=5 and 2n=10
Thus, the number of sides of each polygon is 5 and 10.