# Mathematics

You are designing a rectangular dog pen off the back of your house. The house will form one side of the dog pen. The pen is to have an area of 800 square feet, but you want to minimize the amount of fencing that you need for the three sides of the pen not against the house. This will include an opening that is 4 feet wide where a gate will be placed. How many feet of fencing do you need to build the pen?

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1. L = 2 x + y - 4
800 = x y so y= 800 / x
L = 2 x + 800/x - 4
look for dL/dx = 0
0 = 2 - 800 / x^2
2 x^2 = 800
x = 20
y = 800/20 = 40
L = 40 + 40 - 4 = 66

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👨‍🏫
Damon

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