If the perimeter of a circle is equal to that of a square then the ratio of their areas is

The correct option is B 14 : 11 Let r be the radius of the circle and a be the side of the square. According to the question, Perimter of the circle = Perimeter of the square ⇒ 2 π r = 4 a ⇒ a = π r 2 Area of the circle = π r 2 Area of the square = a 2 Now, ratio of their areas = Area of the circle Area of the square = π r 2 a 2 = π r 2 ( π r 2 ) 2 = π r 2 π 2 r 2 4 = 4 π = 4 22 7 = 28 22 = 14 11 ∴ Option b is correct.

The correct option is B 14 : 11 Calculate the ratios of the areas Let r be the radius of the circle and a be the side of the square. We know that, Perimeter of a circle is 2 π r Perimeter of a square is 4 a Area of circle is π r 2 Area of square is a 2 Using, π = 22 7 Step 1 :- It is given that, Perimeter of a circle = Perimeter of a square ⇒ 2 π r = 4 a ⇒ a = π r 2 Step 2 :- Ratio of their areas = A r e a o f c i r c l e A r e a o f s q u a r e = π r 2 a 2 = π r 2 π r 2 2 = 2 2 × π r 2 π 2 r 2 = 4 π π 2 = 4 π = 4 22 7 = 7 × 4 22 = 28 22 = 14 11 Hence , If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11

Given: The perimeter of a circle is equal to that of a square Formula used: Area of a circle = πr 2 Area of a square = a 2 Perimeter of a circle= 2πr Perimeter of a square = 4a r = radius of the circle a = side of the square Calculation: According to the question: 2πr = 4a ⇒ a =πr/2 Area of circle/area of square =πr 2/a 2 ⇒ Ratio =πr 2/(πr/2) 2 ⇒ Ratio = 4πr 2/π 2r 2 ⇒ Ratio = 4/π ⇒ Ratio = 4 × 7/22 = 14/11 ∴ The ratio of their areas= 14/11 = 14 : 11