Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the blue square (length CD) be 1 unit.
Area Blue is;
1²
= 1 square unit.
a = 180-20-40
a = 120°
(b/sin40) = (1/sin20)
b = 1.87938524157 units.
(c/sin120) = (1/sin20)
c = 2.53208888624 units.
d² = 1²+1.87938524157²-2*1.87938524157cos60
d = 1.62871226577 units.
Area Yellow is;
(1.62871226577)²
= 2.65270364467 square units.
(a) Area Yellow ÷ Area Blue to 2 decimal places is;
2.65270364467 ÷ 1
= 2.65270364467
≈ 2.65
(b) Calculating Length Red ÷ CD
Notice;
CD = 1 unit.
e² = 2(1.87938524157)²
e = 2.65785209755 units.
f = ½(e)
f = 1.32892604878 Units.
g² = 2(1.62871226577)²
g = 2.30334697546 units.
h = ½(g)
h = 1.15167348773 units.
(1.62871226577/sin60) = (1.87938524157/sini)
i = 87.87798714586°
j = i+45
j = 132.87798714586°
k² = 1²+1.15167348773²-2*1.15167348773cos132.87798714586
k = 1.973230804 units.
(1.973230804/sin132.87798714586) = (1.15167348773/sinl)
l = 25.32170253975°
m = 60-l
m = 34.67829746025°
n = m+45
n = 79.67829746025°
It implies;
Length Red (AB) to 2 decimal places is;
√(1.32892604878²+1.973230804²-2*1.973230804*1.32892604878cos79.67829746025
= 2.17255417153 units.
Therefore;
Length Red ÷ Length CD to 2 decimal places is;
2.17255417153 ÷ 1
= 2.17255417153
≈ 2.17
Therefore;
(a) is 2.65
(b) is 2.17
