Question

show that the as largest rectangle with a given perimeter is a square​

Answer 1

HEYA !!!

Step 1:

Let x,y be the length and breadth of a rectangle. Whose permeter is the given value P

∴2(x+y)=p=>y=p2−x

The sides of the rectangle are x,p2−x

Step 2:

The area of the rectangle is

A=x(p2−x)=px2−x2

Step 3:

At extreme values of A,dAdx=0

dAdx=p2−2x

p2−2x=0=>x=p4

d2pdx2=−2<0=>x=p4

Corresponds to a maximum value of A.

∴ the area is maximum when the sides are p4,p4 .

The sides are equal => this is a square