Mathematics Question and Solution
Let b = 1 unit.
Calculating a.
c² = 2a²
c = √(2)a units.
c is the diagonal of each of the three identical squares.
d = c-a
d = (√(2)a-a) units.
It implies;
1² = a²+(√(2)a-a)²-2a(√(2)a-a)cos45
1 = a²+a²-2√(2)a²+2a²-√(2)a(√(2)a-a)
1 = 4a²-2√(2)a²+√(2)a²-2a²
1 = 2a²-√(2)a²
a² = 1/(2-√(2))
a² = ½(2+√(2))
a = √(½(2+√(2))
a = ½√(4+2√(2)) units.
a = 1.30656296488 units.
Therefore;
a÷b is;
½√(4+2√(2))÷1
= ½√(4+2√(2))
= 1.30656296488
