if the perimeters of a square and rectangle are same than..., Area, General Mathematics

Question:If the perimeters of a square and a rectangle are the same, than the areas A and B enclosed by them would satisfy the condition :

A `A < B` 
B `A <= B` 
C `A > B` 
D `A >= B`

/98

+ AnswerC

+ ExplanationLet side of a square = a. length of rect. = x & breadth of rect. = y.

`4a = 2 (x + y) =>(x + y)/2 = a`

Area of square` = a^2 = ((x + y)^2/2)` So, A`= ((x + y)^2/2)`

Area of rect. = xy. So, B = xy.

`(x + y)/2 > x^1/2 y^1/2` [:. A.M. > G.M.]

`=> ((x + y )^2/2)`> xy i. e.A > B.

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