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## 'Eight Ratios' printed from http://nrich.maths.org/

Two perpendicular lines lie across each other and the end points
are joined to form a quadrilateral.

Eight ratios are defined, three are given but five need to be
found.

Each original line is now in two parts and there are a further four
lengths forming the quadrilateral.

The ratios work like this, 0.43 is the ratio between the upper
portion of the vertical line and the hypotenuse of that orange
triangle. Similarly 0.88 is the ratio between the right-hand
portion of the horizontal line and the hypotenuse of that green
triangle.

Can you find the five ratios which were not given?

This problem is about ratio, you could have a big version or a
small version of the diagram and it would make no difference, so
why not make the size something convenient ? Why not try having the
hypotenuse of the top right orange triangle as your unit - ie. make
that length 1 . What will you do next ?