Mathematics Question and Solution
Calculating Blue Area.
Let x be the radius of the inscribed circle.
a = 12+18
a = 30 units.
b = (x+12) units.
c = (x+18) units.
Calculating x.
a² = b²+c²
30² = (x+12)²+(x+18)²
900 = x²+24x+144+x²+36x+324
900 = 2x²+60x+468
2x²+60x-432 = 0
x²+30x-216 = 0
x²+36x-6x-216 = 0
x(x+36)-6(x+36) = 0
(x-6)(x+36) = 0
It implies;
x ≠ -36
x = 6 units.
Again, x is the radius of the inscribed circle.
Therefore, area blue is;
Area square with side 6 units - Area quarter circle with radius 6 units.
(6*6) - (¼*6*6π)
= 36-9π
= 9(4-π) square units.
= 7.72566611769 square units.
