Mathematics Question and Solution
Calculating Area Yellow÷Area Red.
Notice.
Inscribed blue square area is 8 m².
a = √(8)
a = 2√(2) m.
a = 2.82842712475 m.
a is the side length of the inscribed blue square.
Let r be the radius of the inscribed yellow circle.
b = r-a
b = (r-2√(2)) m.
Calculating r.
b²+b² = r²
2(r-2√(2))² = r²
2r²-8√(2)r+16 = r²
r²-8√(2)r+16 = 0
(r-4√(2))² = -16+(-4√(2))²
(r-4√(2))² = -16+32
r-4√(2) = √(16)
r = 4√(2)±4
It implies
r ≠ (4√(2)-4) m.
r = (4√(2)+4) m.
r = 4(√(2)+1) m.
r = 9.65685424949 units.
Again, r is the radius of the inscribed yellow circle.
Area Inscribed yellow circle is;
πr²
= π(4(√(2)+1))²
= 16π(2√(2)+3) m².
= 292.968701393 m².
c = 2r
c = 2(4√(2)+4)
c = 8(√(2)+1) m.
c = 19.313708499 m.
c is the diameter of the inscribed yellow circle and also the side length of the ascribed square.
d² = 2r²
d² = 2(9.65685424949)²
d = √(186.509667992)
d = 13.6568542495 m.
d is half the diagonal of the ascribed square.
Let x be the radius of the inscribed red circle.
e = r-x
e = (9.65685424949-x) units.
f = r+x
f = (9.65685424949+x) units.
Calculating x.
f² = 2e²
(9.65685424949+x)² = 2(9.65685424949-x)²
x = 1.65685424949 m.
Again, x is the radius of the inscribed red circle.
Area inscribed red circle is;
πx²
= π(1.65685424949)²
= 8.62419335122 m².
Therefore,
Area Yellow÷Area Red is;
292.968701393/8.62419335122
= 33.9705627485
≈ 34
