Mathematics Question and Solution
a = 10 units.
a is the radius of the circle.
b = (20-2x) units.
c = ½(b)
c = ½(20-2x)
c = (10-x) units.
It implies;
Calculating x.
10² = 2c²
100 = 2(10-x)²
100 = 200-40x+2x²
2x²-40x+100 = 0
x²-20x+50 = 0
Resolving the above quadratic equation via completing the square approach to get x.
( x-10)² = -50+(-10)²
( x-10)² = 50
x-10 = ±√(50)
x = 10±5√(2)
It implies;
x ≠ 10+5√(2)
x = 10-5√(2) units.
x = 2.9289321881 units.
The length, y of the side of the square is;
y = 2(a)-x
And a = 10 units, x = 10-5√(2) units.
y = 2(10)-(10-5√(2))
y = 20-10+5√(2)
y = 10+5√(2) units.
Again, y is the side length of the square.
