Mathematics Question and Solution
a² = 36
a = 6 cm.
a is the side length of the inscribed big square.
b² = a²+(0.5a)²
b² = 6²+(0.5*6)²
b² = 36+9
b = √(45)
b = 3√(5) cm.
b is the radius of the ascribed semi circle.
Let c be the side length of the inscribed small blue square.
d = ½(a)+c
d = (3+c) cm.
Calculating c.
(3√(5))² = (3+c)²+c²
45 = 9+6c+c²+c²
2c²+6c-36 = 0
c²+3c-18 = 0
Resolving the above quadratic equation via factorization approach to get c, side length of the inscribed blue small square.
c²+6c-3c-18 = 0
c(c+6)-3(c+6) = 0
It implies;
c ≠ -6
c = 3 cm.
Therefore, area of the inscribed blue small square is;
c²
= 3²
= 9 cm²
