Question

If you have 50 feet of fence, what shape would yield the greatest area in yards?

Answer 1

Answer:

Square

Step-by-step explanation:

Perimeter of a rectangle is

P=2(l+w)

Where l is length and w is width

Substituting 50 for P

50=2(l+w)

25=l+w

Making w the subject of formula then

w=25-l

Area is lw and substituting for w

A=l(25-l)=-l²+25l

A=-l²+25l

Getting firat derivative of A with respect to l

-2l+25=0

l=25/2=12.5 yards

Width will be 25-12.5=12.5 yards

The dimensions of length and width are same hence the shape is square