Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let length AB = 2 units.
Therefore;
Side length of the square, x is;
2x² = 2²
x = √(2) units.
It implies;
Area square is;
x²
= √(2)²
= 2 square units.
Area green is;
Area triangle with height √(3) units and base 1 unit - Area triangle with height ⅓√(3) units and base 1 unit - Area triangle with height tan15 units and base 1 unit.
= ½(√(3)*1) - ½(⅓√(3)*1) - ½(tan15*1)
= ½√(3) - (√(3)/6) - ½(tan15)
= ⅓√(3) - ½(2-√(3))
= (5√(3)-6)/6 square units.
Therefore;
Area Green ÷ Area Square exactly is;
(5√(3)-6)/6 ÷ 2
= (5√(3)-6)/12
