Mathematics Question and Solution
Notice!
Since we are resolving to get;
Area Blue/Area Yellow
Let x be 1 unit.
It implies;
Area Yellow is;
1²
= 1 square unit.
Ascribed or bigger square side length is;
1+3(1)
= 1+3
= 4 square units.
Calculating r, radius of the inscribed blue circle.
a = 4-1-r
a = (3-r) units.
b = a
It implies;
r² = 2a²
r² = 2(3-r)²
r² = 2(9-6r+r²)
r² = 18-12r+2r²
r²-12r+18 = 0
Resolving the above quadratic equation via completing the square approach to get r.
(r-6)² = -18+(-6)²
(r-6)² = -18+36
r-6 = ±√(18)
r = 6±3√(2)
It implies;
r ≠ 6+3√(2) units.
r = 6-3√(2) units.
Therefore;
Area Blue is;
πr²
= π(6-3√(2))²
= 9.7022175201 square units.
It implies;
Area Blue/Area Yellow is;
π(6-3√(2))²/1
= π(6-3√(2))² exactly.
= 9.7022175201 exactly in decimal.
