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The area of a region was 125,000 square feet. A type of fencing costing \$20 per foot was used along the back and front, and a less expensive fence costing \$10 was used for the other sides. What were the dimensions of the region that minimized the cost of the fence?

I am not sure where to start with this question, my class has not done anything like this before.I started the equation with the function $$ C=20(2x)+10(2y) $$ And then I used substitution to get $$ C=40x+2500000/x $$ I am not sure how to solve this problem. I looked up an example problem similar; however, they used calculus to solve this and I am only in algebra. Does anyone know how to solve this without calculus?

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    $\begingroup$ You probably noticed that dollar signs in a post do weird things. That is because it is used to initiate inline math mode for MathJax and $\LaTeX$. If you want a dollar sign to appear normally like \$, write it as \$ with the escape character \. $\endgroup$ – JMoravitz Mar 4 at 18:03
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    $\begingroup$ Hint: use AM-GM. $\endgroup$ – Connor Harris Mar 4 at 18:04
  • $\begingroup$ @ConnorHarris What's AM-GM? $\endgroup$ – Jake Miller Mar 4 at 18:20
  • $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$ – Connor Harris Mar 4 at 18:23
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    $\begingroup$ Note that $Ax + \frac{B}{x} \geq 2 \sqrt{AB}$ with equality iff $Ax = \frac{B}{x}$. $\endgroup$ – Connor Harris Mar 4 at 18:28

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