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spayn [35]
3 years ago
8

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
Mathematics
2 answers:
DIA [1.3K]3 years ago
4 0

Answer:

D

Step-by-step 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.

nordsb [41]3 years ago
4 0

Answer:

Step-by-step explanation:

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

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