Mathematics Question and Solution
Calculating the inscribed half circle's diameter.
Let a be the radius of the inscribed half circle.
b = (1+2a) units.
c = (1+a) units.
d²+a² = (1+a)²
d² = 1+2a+a²-a²
d = √(1+2a) units.
Therefore;
Calculating a.
2(12*a)+a*√(1+2a) = 12(1+2a)
24a+√(1+2a)a = 12+24a
√(1+2a)a = 12
a²(1+2a) = 12²
a²+2a³ = 144
2a³+a² = 144
It implies;
a = 4 units.
Therefore, diameter of the inscribed half circle is;
2a
= 2*4
= 8 units.
