What is the biggest rectangle you can make with a perimeter of 30?

Answer 1

let say a is the width and b is the length

then 2(a+b)=30 or (1)a+b=30 and the biggest rectangle is the one having the biggest area

So (2) A=axb should be max

From (1) a=30-b then using (2) A=(30-b)*b = 30b-b2

So the next point is to study the function f(x)=30x-x2

it's derivative is f'(x)=30-2x which change sign at 30/2=15

so 15 is the maximum

The maximum area is 225, b=15 then a=15

Then the biggest rectangle with a perimeter of 30 is a square!