Mathematics Question and Solution
Let the inscribed square side be a.
Radius of the half circle is 5 units.
Considering Similar Triangle Ratios.
5 = a
a = (5-a)
Cross Multiply.
25-5a = a²
a²+5a-25 = 0
(a+(5/2))² = 25+(5/2)²
a+(5/2) = √(25+(25/4))
a+(5/2) = √(125/4)
a = -(5/2)±½(5√(5))
a ≠ -½(5+5√(5)) units.
a = ½(5√(5)-5) units.
Therefore;
Area of the inscribed square is;
a²
= (½(5√(5)-5))²
= ¼(125-50√(5)+25)
= ¼(150-50√(5)) square units.
= 12.5(3-√(5)) square units.
= 9.54915028125 square units.
