Mathematics Question and Solution
Let the side length of the green square be x.
Notice, radius of the two congruent circles is 5 units each.
Therefore;
a = (5-x) units.
b = (5-½(x)) units.
Observing Pythagoras Rule to get x, side length of the green square.
5² = b²+a²
5² = (5-½(x))²+(5-x)²
25 = 25-5x+(x²/4)+25-10x+x²
0 = 25-15x+(5x²/4)
5x²-60+100 = 0
x²-12x+20 = 0
Resolving the above quadratic equation via completing the square approach.
(x-6)² = -20+(-6)²
(x-6)² = 16
x = 6±√(16)
x = 6±4
It implies;
x ≠ 10 units.
x = 2 units.
Therefore, green square area is;
x²
= 2²
= 4 square units.
