Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the inscribed regular pentagon be 2 units.
Therefore;
Length Red (AD) is;
2+2(2cos72)
= 2+4cos72
= 3.2360679775 units.
Calculating Length Blue.
Let the radius of the inscribed circle be r.
r is;
tan27 = r/(3.2360679775-2sin72-r)
tan27=r/(1.33395494491-r)
0.67968399291=1.50952544949r
r = 0.45026335471 unit.
Length Blue is;
1.1163084098tan54 + r
1.1163084098tan54+0.45026335471
= 1.98673006763 units.
It implies;
Length Blue ÷ Length Red to 2 decimal places is;
1.98673006763 ÷ 3.2360679775
= 0.61393335413
≈ 0.61
