Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he use? What will be the area of the garden?

Question

mathmale · Answer

Draw a picture representing this (rectangular) garden.  Label the Length and Width:  L and W.  

Write a formula for the Perimeter of this garden in terms of L and W.

Create a formula for the area:  A = L*W.  How is L related to W?  If you can answer that, you can then eliminate either L or W.

Ask questions if this is not sufficiently clear for you.

skullpatrol · Answer

But the question asks for the greatest possible area?

mathmale · Answer

That's right.  The perimeter is of the same length as is the available fencing, or 376 feet.

skullpatrol · Answer

$$2l + 2w =376$$
$$lw=A$$
How do you maximize A?

mathmale · Answer

Hint:  can you eliminate one of the two variables, l and w?