Mathematics Question and Solution
Calculating Area Blue.
Let a be the side length of the ascribed quarter circle.
tan30 = 2/b
b = 2√(3) units.
c = (a-2) units.
d = (2√(3)+½(a))
d = ½(4√(3)+a) units.
Calculating a.
(a-2)² = (½(4√(3)+a))²+2²
a²-4a+4 = ¼(48+8√(3)a+a²)+4
4a²-16a = 48+8√(3)a+a²
3a²-(16+8√(3))a-48 = 0
3a²-29.8564064606a-48 = 0
Therefore;
a = 11.3605 units.
Again, a is the radius of the ascribed quarter circle.
(11.3605)² = e²+f²
f = √(129.06096025-e²)
e is the side length of the inscribed blue square.
g = f-e
g = (√(129.06096025-e²)-e) units.
h = e-½(a)
h = (e-5.68025) units.
Calculating e.
tan30 = (e-5.68025)/(√(129.06096025-e²)-e)
√(129.06096025-e²)-e = √(3)e-5.68025√(3)
√(129.06096025-e²) = 2.73205080757e-9.83848159969
129.06096025-e² = (2.73205080757e-9.83848159969)²
129.06096025-e² = 7.46410161514e²-53.7584631994e+96.7957201874
8.46410161514e²-53.7584631994e-32.2652400626 = 0
Therefore;
e = 6.90353 units.
Again, e is the side length of the inscribed blue square.
Area inscribed blue square is;
e²
= 6.90353²
= 47.6587264609 square units.
