Question

Find the largest possible rectangular area you can enclose, assuming you have 128 meters of fencing. What is the (geometric) significance of the dimensions of this largest possible enclosure?

Answer 1

Answer:

Step-by-step explanation:

let the length=x

width=y

P=2(x+y)=128

x+y=128/2=64

y=64-x

area A=xy=x(64-x)=64x-x²

$\frac{dA}{dx} =64-2x\\\\\frac{dA}{dx} =0,gives~64-2x=0,x=32\\\frac{d^2A}{dx^2} =-2$

so A or area is maximum if x=32

y=64-32=32

or it is a square of edge=32 meters.