Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the length of the rectangle be 2 units.
Length AB is:
√(2) units.
a² = 2+1-2√(2)cos75
a = √(4-√(3)) units.
(a) Let Alpha be x.
Calculating x.
(1/sinx) = (√(4-√(3))/sin75)
x = asin(sin75/√(4-√(3)))
x = 39.89609063893°
Area yellow is;
Area triangle with height (2√(2)-√(6)) units and base 0.40352376128sin39.89609063893 units
= 0.5*(2√(2)-√(6))*0.40352376128sin39.89609063893
= 0.04903810568 square units.
Area Red is;
Area triangle with height √(2) units and base sin75 units - Area yellow.
= ½*√(2)sin75 - 0.04903810568
= 0.63397459622 square units.
(b) Area Red ÷ Area Yellow exactly in decimal is;
0.63397459622 ÷ 0.04903810568
= 12.92820322948
