Mathematics Question and Solution
Let the side length of the square be 2a cm.
b² = a²
b² = ½(a)²
b = ½√(2)a cm.
b is the radius of the circle.
c² = 2(2a)²
c² = 8a²
c = 2√(2)a cm.
c is the diagonal of the square.
d = c-b
d = 2√(2)a-½√(2)a
d = ½(3√(2)a) cm.
e = PA+PB
e = 5+4
e = 9 cm.
Therefore;
9² = (½√(2)a)²+(½(3√(2)a)²-2*(½√(2)a)(½(3√(2)a)cos135
81 = 0.5a²+4.5a²-3a²cos135
81 = 5a²+2.1213203436a²
81 = 7.1213203436a²
a = √(11.3742952279)
a = 3.3725799068 cm.
2a (side length of the square) is;
2*3.3725799068
= 6.7451598136 cm.
Area Blue Square is;
(2a)²
= 6.7451598136²
= 45.497180911 cm²
