Mathematics Question and Solution
Let the radius of the inscribed red semi circle be r.
Therefore;
(8-r)²+(9-r)²=r²
64-16r+r²+81-18r+r²=r²
r²-34r+145=0
(r-17)²=-145+(17)²
r = 17±√(144)
r = 17±12
It implies ;
r ≠ 29 cm.
r = 5 cm.
Therefore area red inscribed semi circle is;
½π(5)²
= ½(25π) cm²
Area rectangle (green) is;
9 * 8
= 72 cm²
It implies;
Area red inscribed semi circle ÷ Area green rectangle is;
½(25π)÷72
= 25π/144
= 275/504
