Mathematics Question and Solution
Calculating Green Area : Red Area.
Let x be the red square side length.
Let 2 units be the green square red length.
Area green is;
2²
= 4 square units.
Calculating x.
a = (2-x) units.
b = 90-60
b = 30°
tan30 = c/x
c = x/√(3)
c = ⅓(√(3)x) units.
d = x-c
d = x-⅓(√(3)x)
d = ⅓(3-√(3))x units.
It implies;
x ~ ⅓(3-√(3))x
2 ~ (2-x)
Cross Multiply.
⅔(3-√(3)) = 2-x
6-2√(3) = 6-3x
3x = 2√(3)
x = ⅔√(3) units.
Again, x is the side length of the red square.
Area red square is;
x²
= (⅔√(3))²
= 4/3 square units.
Therefore, Green Area : Red Area is;
4 : (4/3)
12 : 4
3 : 1
