Question

you have 288 feet of fencing to enclose a rectangular plot that borders on a river. if you do not fence the side along the river, what is the largest area that can be enclosed?

Answer 1

it needs to look like a square

Answer 2

or as close as a square as it can get

Answer 3

so 96 on the 3 sides

Answer 4

first the answer
take half of the fence and put it parallel to the river
other remaining half gets split between the two sides

Answer 5

@haha1231233123 unfortunately that is not right

Answer 6

and the area of the square is 96 times 96 = 9216.sqft

Answer 7

wouldn't you use a = 2w + l ?

Answer 8

144 by 72

Answer 9

you have \[2x+y=288\] so \(y=288-2x\) and
\[A=xy\] so \[A(x)=x(288-2x)=288x-2x^2\]

Answer 10

max is at the vertex, and first coordinate of the vertex is \(-\frac{b}{2a}=\frac{288}{4}=72\) as promised