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| Math Central | Quandaries & Queries |
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I've tried to solve the problem below but can't seem to get the right answer. Your insight would be much appreciated. I have 60 m to construct a fence adjacent to my house. What are the values of x and y that maximize the area of the yard? |
Hi Andy,
Here is my diagram.
The length of the side of the yard parallel to the house is y meters and the lengths of the other two sides are x meters each. What I know is that
2x + y = 60 and the area of the yard is xy square meters.
Hence y = 60 - 2x and this allows me to write the area of the yard as a function of one variable x. The area of the yard is
A(x) = x(60 - 2x)
This is the function to maximize.
Is that what you got?
Penny
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