Sir Mike Ambrose is the author of the question.
Let the side length of the be 2 units.
Therefore;
BC = 2 units.
It implies;
Area orange is;
½(1*2) = 1 square units.
Area green is;
½(1*2) + ½(2/√(5))(4/√(5))
= 1 + (4/5)
= (9/5)
Therefore;
Area orange : Area green is;
1 : (9/5)
=(5*1) : (5*(9/5))
= 5 : 9
Proved.
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