A polygon has 25 sides, the lengths of which starting from the smallest side are in A.P. If the perimeter of the polygon is 2100 cm and the length of
A polygon has 25 sides, the lengths of which starting from the smallest side are in A.P. If the perimeter of the polygon is 2100 cm and the length of the largest side 20 times that of the smallest, then the length of the smallest side and the common difference of the A.P. is -
A. 8 cm, 6 `(1)/(3)` cm
B. 6 cm, 6 `(1)/(3)`
C. 8 cm, 5 `(1)/(3)` cm
D. None of these
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Correct Answer - A
Let a be the length of smallest side and d cm the common difference ltBrgt Now `S_(n)=(n)/(2)[2a+(n-1)d]`
n = 25, `S_(25)= 2100` ltBrgt `2100=(25)/(2)[2a+24d]" "...(1)`
a+12d = 84
`because` The largest side = `25^(th)` side ltBrgt =a+24d = 20a `" "...(2)`
solve (1) and (2)
a = 8 , d = `6(1)/(3)`
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