Mathematics Question and Solution
Calculating Shaded Blue Area.
Let x be the radius of the inscribed circle.
a = (12+x) units.
a is the height of the ascribed triangle.
b = (18+x) units.
b is the base of the ascribed triangle.
c = 12+18
c = 30 units.
c is the hypotenuse of the ascribed triangle.
Calculating x.
(18+x)²+(12+x)² = 30²
324+36x+x²+144+24x+x² = 900
2x²+60x+468 = 900
2x²+60x-432 = 0
x²+30x-216 = 0
(x+15)² = 216+15²
(x+15)² = 441
x = -15±√(441)
x = -15±21
It implies;
x ≠ -15-21
x = -15+21
x = 6 units.
Again, x is the radius of the inscribed circle.
It's implies, area blue is;
Area square with side length 6 units - Area quarter circle with radius 6 units.
6²-(¼*6*6π)
= 36-9π
= 9(4-π) square units.
= 7.72566611769 square units.
