Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Area Green is;
Area triangle with height √(8(31-14√(3))) units and base √(178-72√(3))sin57.72115346403 units.
= 0.5*√(8(31-14√(3)))*√(178-72√(3))sin57.72115346403
= 22.67949192422 square units.
Area Red is;
Area triangle with height 5√(2) units and base 6√(2) units + Area triangle with height ⅕(11√(29)) units and base ⅕(27sin(atan(5/2))) units.
= ½*5√(2)*6√(2) + ½*⅕(11√(29))*⅕(27sin(atan(5/2)))
= 30 + (297/10)
= 597/10 square units.
Therefore;
Area Green ÷ Area Red exactly as a single fraction is;
22.67949192422 ÷ (597/10)
= 2150355800/5660454903
= 0.37989098701 exactly in decimal.
