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Iran Contests
Iran MO (3rd Round)
2004 Iran MO (3rd Round)
7
7
Part of
2004 Iran MO (3rd Round)
Problems
(1)
Easy
Source: Iran 2004
9/18/2004
Suppose
F
F
F
is a polygon with lattice vertices and sides parralell to x-axis and y-axis.Suppose
S
(
F
)
,
P
(
F
)
S(F),P(F)
S
(
F
)
,
P
(
F
)
are area and perimeter of
F
F
F
. Find the smallest k that:
S
(
F
)
≤
k
.
P
(
F
)
2
S(F) \leq k.P(F)^2
S
(
F
)
≤
k
.
P
(
F
)
2
geometry
perimeter
inequalities
ratio
rectangle
geometry proposed