Mathematics Question and Solution
Calculating Inscribed Area Blue Square.
Let x be the side length of the blue square.
tan60 = x/a
√(3) = x/a
a = ⅓(√(3)x) units
b = a+x
b = ⅓(√(3)x)+x
b = ⅓(√(3)x+3x) units.
Calculating x².
10² = x²+(⅓(√(3)x+3x))²
100 = x²+⅑(3x²+6√(3)x²+9x²)
100 = x²+⅓(x²+2√(3)x²+3x²)
300 = 3x²+x²+2√(3)x²+3x²
300 = 7x²+2√(3)x²
(7+2√(3))x² = 300
x² = 300/(7+2√(3)) square units.
x² = 28.6694463637 square units.
x² is the area of the inscribed blue square.
