Mathematics Question and Solution
Calculating Area Inscribed Blue Square.
a² = 4²-2²
a = √(12)
a = 2√(3) units.
b = 2a
b = 4√(3) units.
Let x be the side length of the inscribed blue square.
x+c+c = 4
x+2c = 4 --- (1).
d = ½(x+2c) units.
4² = (x+c)²+(½*x)²
16 = x²+2xc+c²+¼(x²)
64 = 5x²+8xc+4c² --- (2).
At (1).
x+2c = 4
x = (4-2c) --- (3).
Calculating c.
Substituting (3) in (2).
64 = 5(4-2c)²+8(4-2c)c+4c²
64 = 5(16-16c+4c²)+32c-16c²+4c²
64 = 80-80c+20c²+32c-16c²+4c²
64 = 80-48c+8c²
c²-6c+10 = 8
c²-6c+2 = 0
(c-3)² = -2+(-3)²
(c-3)² = 7
c = 3±√(7)
It implies;
c ≠ 3+√(7) units.
c = 3-√(7) units.
c = 0.35424868894 units.
Calculating x, side length of the blue inscribed square.
Recall.
At (3).
x = (4-2c)
And c = (3-√(7)) units.
x = 4-2(3-√(7))
x = 4-6+2√(7)
x = 2√(7)-2
x = 2(√(7)-1) units.
x = 3.29150262213 units.
Again, x is the side length of the inscribed blue square.
Therefore, area inscribed blue square is;
x²
= (2√(7)-2)²
= 8(4-√(7)) square units.
= 10.8339895115 square units.
