Find the side of a maximum size square which can be inscribed in a semi-circle of radius r cm.

  1. 3r/√5 cm
  2. 2r/√5 cm
  3. r/√5 cm
  4. 4r/√5 cm

Answer (Detailed Solution Below)

Option 2 : 2r/√5 cm
Free
SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 02 Aug 2023 Shift 1)
100 Qs. 200 Marks 60 Mins

Detailed Solution

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Given:

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 cm

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