Question

If a square and a rectangle having the same perimeter and their areas are s and r respectively then

Answer 1

Given :  a square and a rectangle having the same perimeter .  their areas are s and r respectively

To find : relation between s & r

Solution

a square and a rectangle having the same perimeter

Let say Perimeter  = P  

Then side of  Square = P/4

Area of square s  = (P/4)² = P²/16

Length of rectangle = L

Then Breadth of rectangle =  (P  - 2L ) /2    

Area r  = L ( P - 2L)/2

r = LP/2  -  L²

dr/dL =  P/2 - 2L

=> L = P/4

d²r/dL² = - 2 < 0

Hence r is maximum when   L = P/4

& B =  (P  - 2L ) /2      = P/4 Hence Square  

so area of Square ≥ area of rectangle   ( equal to sign is also there because square is also a special type of rectangle )

s ≥ r  

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Answer 2

Given :  a square and a rectangle having the same perimeter .  their areas are s and r respectively

To find : relation between s & r

Solution

a square and a rectangle having the same perimeter

Let say Perimeter  = P  

Then side of  Square = P/4

Area of square s  = (P/4)² = P²/16

Length of rectangle = L

Then Breadth of rectangle =  (P  - 2L ) /2    

Area r  = L ( P - 2L)/2

r = LP/2  -  L²

dr/dL =  P/2 - 2L

=> L = P/4

d²r/dL² = - 2 < 0

Hence r is maximum when   L = P/4

& B =  (P  - 2L ) /2      = P/4 Hence Square  

so area of Square ≥ area of rectangle   ( equal to sign is also there because square is also a special type of rectangle )

s ≥ r  

Learn more:

Show that out of all rectangles with given area a square has ...

https://brainly.in/question/11774641

Rohit wants to design a rectangular park of perimeter and area Then ...

https://brainly.in/question/17303098