What is the minimum perimeter of a rectangle with an area of 676 m^2
Call the sides a , b
So
ab = 676
b = 676/a
Perimeter = 2 ( a + b)
P = 2 ( a + 676 / a )
P = 2a + 1352 / a take the derivative and set to 0
P' = 2 - 1352/a^2 = 0
2 = 1352/a^2
a^2 = 1352 / 2
a^2 = 676
a = 26
b = 676 / 26 = 26
Min perimeter = 2 ( 26 + 26) = 104
(1, 676)=> 1+1+676+676 = 1354
(2, 338)=> 2+2+338+338 = 680
(4, 169)=> 4+4+169+169 = 177
(13, 52)=> 13+13+52+52 = 130
(26, 26)=> 26+26+26+26 =104
