Discussion
The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?
Answer: A
The circle has the largest area.
Give all three shapes the same perimeter P and compare their areas:
- circle: radius \(P/2\pi\), area \(P^{2}/4\pi \approx 0.0796P^{2}\)
- square: side \(P/4\), area \(P^{2}/16 = 0.0625P^{2}\)
- equilateral triangle: side \(P/3\), area \(\frac{\sqrt{3}}{4}(P/3)^{2} \approx 0.0481P^{2}\)
The circle wins, and this is a general rule: among all plane figures with a given perimeter, the circle encloses the most area. The square comes second and the triangle last, so the statements naming the square or the triangle are false, and the areas are clearly not equal.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development