Farmer Ed has 6500 meters of fencing and want to enclose a r

Farmer Ed has 6,500 meters of fencing, and want to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side alog the river, what is the largest area that can be enclosed?

Solution

Only one side of is not beig fenced.So if length =l and width =w

Length of fence = l +2w = 6500

Area = l*w = (6500 -2w)w

= -2w^2 +6500w

Max. Area is found at vertex x= -b/2a for ax^2 +bx +c

w = -(6500)/(-2*2) = 1625 mt

l= 6500 -2*1625 = 3250 metres

Largest Area =5281250 mt^2