Mathematics Question and Solution
Let AB be x cm.
BC = 3x cm.
AC = AB+BC
AC = 4x cm.
sin60 = a/16
a = 8√(3) cm.
a is AC.
Therefore;
4x = 8√(3)
x = 2√(3) cm.
Again, x is AB.
BC = 6√(3) cm.
CE = CD = 8 cm.
tanb = 8/(6√(3))
b = atan(4/(3√(3)))°
tanb = c/x
4/(3√(3)) = c/(2√(3))
c = ⅓(8) cm.
d = 180-60-atan(3√(3)/4)
d = 67.589089469°
((8/3)/sin67.589089469) = (e/sin60)
e = 2.4980718188 cm.
Area red is;
½*(8/3)*2.4980718188sin(atan(3√(3)/4)
= 2.6393155163 cm²
Area green is;
½*(8/3)*16sin60-Area red.
= 18.4752086141-2.6393155163
= 15.8358930978 cm²
Therefore;
Area Red ÷ Area Green exactly in decimal is;
2.6393155163÷15.8358930978
= 0.1666666667
= ⅙ exactly in fraction.
