Question

If the farmer has 152 feet of fencing, what are the dimensions of the region with the largest area?

Answer 1

What's the shape of what the farmer is fencing?

Answer 2

Answer:

square of  each side=38 ft

Step-by-step explanation:

square has the largest area.

each side=152/4=38ft

alternatively

let x and y be the sides

2x+2y=152

x+y=76

y=76-x

area A=xy=x(76-x)=76x-x²

$\frac{dA}{dx} =76-2x\\\frac{dA}{dx} =0,gives ~76-2x=0\\2x=76\\x=76/2=38 \\\frac{d^2A}{dx^2} =-2$