Question

what are the deminisions of a rectangle of maximum arear using 240m of fencing

Answer 1

Perimeter=2x+2y
Given Perimeter=240,
2x+2y=240
y=120-x
----------------------
Area, A=xy
A=x(120-x)
A=120x-x^2
\[\frac{dA}{dx}=120-2x\]
\[For ~~maximum~~ area, ~\frac{dA}{dx}=0\]
So,
120-2x=0
x=60

y=120-x
y=120-60
y=60