Mathematics Question and Solution
Let the side length of the two congruent inscribed squares be 1 unit each.
a² = 1+2²
a = √(5) units.
a is the radius of the half circle.
tanb = (½)
b = atan(½)°
(√(5)/sin(atan(½))) = (2/sinc)
c = 23.5781784782°
d = 180-c-atan(½)
d = 129.8567703447°
e = d-90
e = 39.8567703447°
Area B (Area Orange Triangle) is;
0.5*√(5)sin39.8567703447
= 0.716515139 square units.
f = 129.8567703447-atan(½)
f = 103.2917191676°
g = 0.5*√(5)²sin103.2917191676
g = 2.433030278 square units.
Area A (Area Green Triangle) is;
g - Area B - (½*1*2)
= 2.433030278-0.716515139-1
= 0.716515139 square units.
Therefore;
Area A ÷ Area B is;
0.716515139÷0.716515139
= 1
