From the given data,

No of sides n = 20

Perimeter of the polygon i.e, sum of the total sides s = 2600

Let us consider smallest side be a

Largest side is 12 times that of the smallest side

∴ largest side = 12 a

By using sum of A.P formula, we get

Largest side = a + (n - 1) d = 12 a

Sum = n/2 × [2a + (n - 1)d] = n/2 × [ a + a + (n - 1)d] = n/2 × [a + 12a]

s = n/2 × (13a)

By substituting the value of s = 2600 and n = 20 ,we get

⇒ 2600 = 20/2 × (13a)

⇒ 2600 = 10 (13a)

⇒ 260 = 13 a

⇒ smallest side a = 20 cm and largest side 12a = 12 × 20 = 240 cm

We know that largest side = a + (n - 1)d = 12a = 240

⇒ 240 = 20 + (20 - 1)d

⇒ 220 = 19 d

⇒ d = 220/19 = 11.57 cm