Mathematics Question and Solution
Calculating Area Green Inscribed Square.
Let x be the side length of the green square.
a² =2x²
a = √(2)x units.
a is the radius of the ascribed half circle.
b² = (√(2)x)²+x²
b² = 2x²+x²
b = √(3)x units.
c = 2+b
c = (2+√(3)x) units.
Calculating x.
It implies;
(2+√(3)x) ~ √(2)x
2√(2)x ~ √(3)x
Cross Multiply.
4x² = 2√(3)x+3x²
x² = 2√(3)x
x = 2√(3) units.
Again, x is the side length of the inscribed green square.
Therefore, area inscribed green square is;
x²
= (2√(3))²
= 12 square units.
