Question
Download Solution PDFFind the side of a maximum size square which can be inscribed in a semi-circle of radius r cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of semi-circle = r cm
Formula used:
Pythagoras theorem
H2 = P2 + B2
Area of square = side2
Calculation:
Let the side of the square be ‘a’ cm
The maximum size square exists with side ‘r’ cm.
⇒ H2 = P2 + B2
⇒ r2 = a2 + (a/2)2
⇒ r2 = a2 + a2/4
⇒ r2 = 5a2/4
⇒ a = 2r/√5
∴ side of maximum size square is 2r/√5 cmLast updated on May 28, 2025
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