Mathematics Question and Solution
Calculating x, side length of the square.
a² = 2x²
a = √(2)x units.
a is BD, diagonal of the square.
tanb = x/(0.5x)
b = atan(2)°
c = 2b
c = 2atan(2)°
c is angle DEF.
d² = 2(0.5x)²-2(0.5x)²cos(2atan(2))
d = 0.894427191x units.
d is DF.
e = ½(180-2atan(2))
e = 26.5650511771°
e is angle EDF.
f = 90-45-26.5650511771
f = 18.4349488229°
f is angle FDB.
Therefore;
x, the square side is;
0.5*0.894427191x*√(2)xsin18.4349488229 = 20
0.2x² = 20
(x²/5) = 20
x² = 100
x = √(100)
x = 10 units.
