Question

proove that if the permeter of rectangle and square are equal the area of rectangle is greater than the area of square

Answer 1

ATQ,
2(a+b) = 4q
where
a,b are sides of rectangle, q is side of square.
so
a+b=2q.......(i)
now,
area of rectangle is a.b
and area of square is q² = ¼(a+b)²,
now let's fix a to some constant value , let a=1,
then ar(rectangle)=b
and ar(sq.)=¼(1+b)²=¼(1+b²+2b)

clearly, [¼+(b/2)²+b] > b