Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the two equal length of the inscribed isosceles triangle (red area) be 2 unit.
Therefore;
Area blue will be;
Area triangle with lengths 1 unit and ⅔ unit, and angle 60°, the angle they form.
= ½(1*⅔sin60)
= (√(3)/6) square unit.
Area red will be;
2(area triangle with height 1 unit and base √(3) unit).
= 2x½(1x√(3))
= √(3) square unit.
Area green will be;
2(area triangle with height 2 unit and base ⅔(√(3)) unit).
= 2x½(2x⅔(√(3)))
= ⅓(4√(3)) square unit.
The exact ratio of the Areas;
Blue : Red : Green is;
√(3)/6 : √(3) : ⅓(4√(3))
= (1/6) : 1 : (4/3)
= 1 : 6 : 8
