Mathematics Question and Solution
Calculating r, radius of the half circle.
Let x be the diameter of the half circle.
x² = 16²+a²
a = √(x²-256) units.
b = a-21
b = (√(x²-256)-21) units.
c = (x-7) units.
Calculating x.
7(x-7) = 21(√(x²-256)-21)
7x-49 = 21√(x²-256)-441
7x+392 = 21√(x²-256)
(7x+392)² = 44x²-112896
49x²+5488x+153664 = 441x²-112896
392x²-5488x-266560 = 0
It implies;
x ≠ -20 units.
x = 34 units.
Again, x is the diameter of the half circle.
Therefore r, radius of the half circle is;
½(x)
r = ½(34)
r = 17 units.
