Mathematics

Problem

A gardener is fencing a rectangular plot using exactly

60\,\text{m}

of fencing wire. a. (i) If the length of the plot is

\ell

metres and the breadth is

b

metres, express the area

A

of the plot in terms of

\ell

and

b

given that

2(\ell+b)=60

. b. (ii) Show that the area

A

attains a maximum value for a particular choice of

\ell

and

b

. c. (iii) Find the maximum possible area of the plot and the dimensions for which it is obtained.