a rectangular area is to be fenced off with 200 meters of fencing. find the dimensions of the rectangle of maximum area that can be fenced off and what is the maximum area?

Question

anonymous · Answer

You want to maximize the area and the area of a rectangle is equal to length times width. So..
$$A=l*w$$
perimeter is twice the length plus twice the width
$$P=2w+2l$$
Since we know what the perimeter is, we can solve the perimeter equation for one variable. So...$$w=(200-2l)/2$$
Now in the area equation, substitute the variable w with the expression we derived from the perimeter formula. So we have...$$A=((200-2l)/2)*l$$
Now differentiate the above equation and solve for zero. the answer you get should be width is equal to 50 as is the length.

anonymous · Answer

thanks u

anonymous · Answer

i got a l=100

anonymous · Answer

hmm..let me rework it.a

anonymous · Answer

i solved for the w and the L=100

anonymous · Answer

ok never mind. you are right it is 50. if w=100 then 2l=100/2 which means l=50