Question

You have 64 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river find the length and width of the plot will maximize the area.

A) length: 33 feet, width: 32 feet
B) length: 16 feet, width: 16 feet
C) length: 48 feet, width: 16 feet
D) length: 32 feet, width: 16 feet

Answer 1

Explanation:

`2L+W=64\\ \\ W=64-2L\\ \\ A=LW\\ \\ A=64L-2L^2\\ \\ (dA)/(dL)=64-4L=0\\ \\ 4L=64\\ \\ L=16\\ \\ W=64-2(16)\\ \\ W=32\\ \\ \text{So the lengths are 32ft by 16ft}`

Answer 2

D

Explanation:

You don't need any real math to guess at the right answer.

Choice A requires at least 33+32+32=97 feet of fence, hence you an rule it out because that is more fence than you have.

Choice B requires at least 16+16+16=48 feet, hence you can rule it out because it does not use all your fence and you can get more area by using it all.

Choice C requires at least 48+16+16=80 feet of fence, which is more than you have.

Choice D requires at least 32+16+16=64 feet of fence, so this is the right choice.