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