Question

if the perimeter of a square and a rectangle are equal which of the two has greater area​

Answer 1

If the perimeter of a square and a rectangle are equal, area of a square is greater than that of a rectangle.

1) We consider the length and breadth of a rectangle are l and b units,  

Area of rectangle (Ar)= l*b units^2....(1)  

2) Given condition in the question:-  

Perimeter of a square = perimeter of a rectangle.

3) So,

4*side = 2*(l+b).  

or. Side of a square = (l+b)/2 units.  

4) Area of square (As) = {(x+y)^2}/4 units ^2....(2)  

5) Subtracting eqn. (2) from eqn. (1)

Ar - As ={lb - (l^2+b^2+2.lb)/4. } units ^2.= {(4.lb-l^2-b^2-2.lb)/4} units ^2.

Ar-As = - (l^2+b^2 - 2.lb)/4 units ^2 = - {(l-b)^2}/4 units ^2

Therefore, Ar - As = negative. Thus As > Ar.  

6) Or. Area of the square greater than area of the rectangle.

Answer 2

Answer:

square has greater side