A rectangular lot is to be fenced using 80m of fencing. What is the maximum area and what are the dimensions of the lot?

Answer 1

P=Perimeter

A=Area

P=2a+2b

80=2a+2b Divide both sides with 2

40=a+b

40-b=a

a=40-b

A=a*b

A=(40-b)*b

A=40b-b^2

dA/dB=40-2b

Function has maximum where first derivation=0

and second derivation<0

First derivation:

dA/dB=40-2b=0

40=2b Divide booths sides with 2

20=b

b=20m

a=40-b=40-20=20m

Second derivation= -2

For a=20m and b=20m rectangle with maximum area is a square.

A(max)=20*20=400m^2