Mathematics Question and Solution
Calculating Blue Area.
Let x be the radius of the ascribed half circle.
a²+7² = (2x)²
a = √(4x²-49) units.
b = a-4
b = (√(4x²-49)-4) units.
It implies;
Calculating x.
√(4x²-49) ~ x
2x ~ (√(4x²-49)-4)
Cross Multiply.
2x² = 4x²-49-4(√(4x²-49)
4(√(4x²-49) = 2x²-49
16(4x²-49) = (2x²-49)²
64x²-784 = 4x⁴-196x²+2401
4x⁴-260x²+3185 = 0
It implies;
x² = 48.6245
Or
x² = 16.3755
Therefore;
x ≠ √(16.3755) units.
x = √(48.6245) units.
x = 6.97312698866 units.
Again, x is the radius of the half circle.
c = 2x
c = 13.9462539773 units.
c is the diameter of the half circle.
sind = 7/13.9462539773
d = 30.12756465°
tan30.12756465 = e/6.97312698866
e = 6.97312698866tan30.12756465
e = 4.04666359623 units.
e is the side length of the inscribed blue square.
Area inscribed blue square is;
e²
= 4.04666359623²
= 16.3754862611 square units.
