Mathematics Question and Solution
Notice;
Blue area = yellow area.
Let the single side length of blue area be 2 units.
Let the single side length of red area be y.
Therefore;
Tanx=y/(4+y) ------ (1)
Tanx=2/(2+y) ------ (2)
Equating (1) and (2)
y/(4+y)=2/(2+y)
8+2y=2y+y²
y²=8
y=2√(2).
Therefore;
Considering equation (2), and y=2√(2).
Angle a will be;
180-2(angle x)
And angle x is;
Tan-¹(2/(2√(2)+2))
It implies;
180 - 2(tan–¹(2/(2√(2)+2)))
= 180 - 2tan-¹(1/(√(2)+1))
= 180 - 2(22.5)
= 180 - 45
= 135°
