Mathematics

Problem

A rectangular plot of land is to be fenced on all four sides using exactly

120\,\text{m}

of fencing wire. Let the length of the plot be

x\,\text{m}

and the breadth be

y\,\text{m}

. a. (i) Express the area

A(x)

of the plot solely in terms of

x

. b. (ii) For

0 < x < 60

, find the value of

x

that yields the maximum possible area of the plot. c. (iii) State the maximum area that can be enclosed with the given amount of fencing.