A farmer has 684 meters of fencing available to enclose a rectangular portion of his land. Only 3 sides require fencing.

Question

(a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river.

 

(b) For what value of x is the area largest?

Answer 1

the rectangle giving the largest area will be a square

684/4=171

you want a square 171 m on each side

however, one side is facing the river and needs no fencing

take the 171 m you would have used for this side and add it to the opposite side getting 171+171=342 m

you have a rectangle 171 m, 342 m, and 171 m for the lengths of the sides

A=lw

A=342*171

A=58,482 sq m

notice that this rectangle is really two squares side by side each one being 171x171

171*171=29,241 sq m

29,241+29,241=58,482