Mathematics Question and Solution
Calculating a/b.
Let r be the equal radius of the inscribed circle and half circle.
It implies;
r = ½(a) units.
c = (a+b) units.
c is the radius of the ascribed quarter circle.
Let c be 1 unit.
d = (1-½(a)) units.
Calculating a.
(1-½(a))² = a²+(½(a))²
1-a²+¼(a²) = a²+¼(a²)
1 = 2a²
a² = ½
a = ½√(2) units.
Calculating b.
Recall.
a+b = c
And c = 1 unit.
Therefore;
a+b = 1
And a = ½√(2) units.
It implies;
b = 1-a
b = 1-½√(2)
b = ½(2-√(2)) units.
Therefore a/b is;
(½√(2))/(½(2-√(2)))
= √(2)/(2-√(2))
= 1+√(2)
= 2.41421356237
