Mathematics Question and Solution
Calculating x²/y².
Let the inscribed blue square side length be 2 units.
Therefore;
y = 2 units.
y² = 4 square units, the area of the blue inscribed square.
Calculating x², the area of the yellow inscribed square.
tana = 2/1
a = atan(2)°
b = 90-a
b = atan(½)°
c² = 2²+1²
c = √(5) units.
d = c-x
d = (√(5-x) units.
It implies;
1 ~ (√(5-x)
2 ~ x
Cross Multiply.
x = 2√(5)-2x
3x = 2√(5)
9x² = 20
x² = 20/9 square units.
Again, x² is the area of the yellow inscribed square.
Therefore;
x²/y² is;
(20/9)/4
= 20/36
= 5/9
