Q19 of 99 Page 264

If a square and a rectangle having the same perimeter and their areas are S and R respectively then

Let the rectangle have dimensions L and B

We know,


Perimeter = 2(L + B), Area = L × B


⇒ R = LB


Let the square have side as ‘a’


We know,


Perimeter = 4a, Area = a2


Given,


Perimeter of square = Perimeter of rectangle


⇒ 2(L + B) = 4a


⇒ L + B = 2a



Now, Area of square





Adding and subtracting from RHS




Since, , [Being a square]


⇒ S > R

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