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I am having trouble solving a math problem for a test review. Here it is:

What are the dimensions of the largest area of a rectangle with a semicircle on a short side given 80ft of fencing?

I am assuming the figure looks like this:

+-------------+ +  +             +  + +             +    + +             +  + +-------------+ +                  ^^^^^                a semi circle 

Can someone please tell me how to solve this problem step by step?

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    Let the side of the rectangle with the semicircle attached and its opposite side be $a$ and let the other two sides be $b$. Can you see why $Area = ab + \frac{1}{2} \pi (\frac{a}{2})^2$ and $a + 2b + \pi \frac{a}{2} = 80$? After that, can you express the area in terms of just $a$ and find the maximum of the quadratic?2011-11-16
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    is [this](http://i.imgur.com/2jsKi.jpg) your figure ?2011-11-16
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    You were very impatient for someone to answer. Now someone has answered - and you have nothing to say?2011-11-16

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