Jack plans to make rectangular garden by having 200 ft of fencing. What are the dimensions of garden with maximum area.

Question

D1=___?___feet, D2=___?___feet

PLEASE HELP ME AND THANK YOU IF YOU DO!!!! PLEASE HELP!!!

Answer 1

the maximum area is always a square

200/4=50

50 feet by 50 feet

if you need work...

P=2l+2w

200=2l+2w

100=l+w

l=100-w

A=l*w

A=(100-w)*w

A=100w-w^2

this is a parabola opening down so it has a maximum point, its vertex (h,k)

h=-b/2a

h=-100/[-2]

h=50

you find k by plugging in 50 for h and k will be the maximum area

A=100*50-50^2

A=5000-2500

A=2500

but from above we have A=50*50 and A=2500 sq ft