Mathematics Question and Solution
Let the pentagon side length be 1 unit.
a = ½(180-108)
a = 36°
b² = 2-2cos36
b = 0.6180339887 units.
Calculating red length (circumference of the inscribed red circle).
Let the radius of the re inscribed circle be r.
Calculating r.
c = ½(180-36)
c = 72°
Therefore;
½(0.6180339887r+2r) = ½*sin36
2.6180339887r = sin36
r = 0.2245139883 units.
Therefore, length red is;
2πr
= 2*0.2245139883π
= 1.4106629925 units.
Calculating blue length.
d² = 2-2cos108
d = 1.6180339887 units.
1.6180339887² = 0.5²+e²
e = 1.5388417685 units.
tan36 = f/0.5
f = 0.363271264 units.
g = e-f
g = 1.5388417685-0.363271264
g = 1.1755705045 units.
Therefore;
Length Red ÷ Length Blue to 2 decimal places is;
1.4106629925÷1.1755705045
= 1.199981615
= 1.20
