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## 'Rhombus in Rectangle' printed from http://nrich.maths.org/

Take any rectangle $ABCD$ such that $AB > BC$. The point $P$
is on $AB$ and $Q$ is on $CD$. Show that there is exactly one
position of $P$ and $Q$ such that $APCQ$ is a rhombus.

Show that if the rectangle has the proportions of A4 paper
($AB=BC$ $\sqrt 2$) then the ratio of the areas of the rhombus and
the rectangle is $3:4$. Show also that, by choosing a suitable
rectangle, the ratio of the area of the rhombus to the area of the
rectangle can take any value strictly between $\frac{1}{2}$ and
$1$.