If a square and a circle have the same perimeter. Which one will have the bigger area?

Mathematics

  • Bernard
  • 12 जुलाई
  • 7941 दृश्य
  • 36 उत्तर
Your Answer

If the perimeter is fixed the circle will have the maximum area possible compared to any other shape including that of square.
We can check that as follows.
Let P be perimeter then, 
P = 2*π*radius {For Circle} = 4*side {For Square)
therefore
Circle Area = π*radius^(2) = π*(P/(2π))^(2) = P^2/(4π) = 0.07958*P^(2)
Square Area = side^(2) = (P/4)^(2) = P/16 = 0.0625*P^(2)
hence
Circle Area > Square Area

0
gre
मॉक परीक्षण अभ्यास के लिए
gre