Math CentralQuandaries & Queries


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?

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