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2008 JBMO Shortlist
8
2008 JBMO Shortlist G8
2008 JBMO Shortlist G8
Source: 2008 JBMO Shortlist G8
October 10, 2017
geometry
JBMO
Problem Statement
The side lengths of a parallelogram are
a
,
b
a, b
a
,
b
and diagonals have lengths
x
x
x
and
y
y
y
. Knowing that
a
b
=
x
y
2
ab = \frac{xy}{2}
ab
=
2
x
y
, show that
(
a
,
b
)
=
(
x
2
,
y
2
)
\left( a,b \right)=\left( \frac{x}{\sqrt{2}},\frac{y}{\sqrt{2}} \right)
(
a
,
b
)
=
(
2
x
,
2
y
)
or
(
a
,
b
)
=
(
y
2
,
x
2
)
\left( a,b \right)=\left( \frac{y}{\sqrt{2}},\frac{x}{\sqrt{2}} \right)
(
a
,
b
)
=
(
2
y
,
2
x
)
.
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