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)
2.6 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF

Given:

Radius of semi-circle = r cm

Formula used:

Pythagoras theorem

H2 = P2 + B2

Area of square = side2

Calculation:

F1 Ashish Shraddha 17.11.2020 D3

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
Latest SSC CHSL Updates

Last updated on May 28, 2025

-> The SSC has released the SSC CHSL exam calendar for various exams including CHSL 2025 Recruitment. As per the calendar, SSC CHSL Application process will be active from 23rd June 2025 to 18th July 2025. 

-> The Exam Date for the SSC CHSL 2025 will be from 8th September 2025 to 18th September, 2025. 

-> The SSC CHSL is conducted to recruit candidates for various posts such as Postal Assistant, Lower Divisional Clerks, Court Clerk, Sorting Assistants, Data Entry Operators, etc. under the Central Government. 

-> The SSC CHSL Selection Process consists of a Computer Based Exam (Tier I & Tier II).

-> To enhance your preparation for the exam, practice important questions from SSC CHSL Previous Year Papers. Also, attempt SSC CHSL Mock Test.  

More Plane Figures Questions

Get Free Access Now
Hot Links: teen patti game online teen patti star apk teen patti master apk best