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## anonymous 5 years ago A lawn has area of 64 sq meters. A straight rope is strung from one corner of the rectangle to the midpoint of one of the two more distant sides of the lawn. What is the minimum possible length of this rope? A. 4 m B. 8 m C. 16 m D. 32 m

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1. anonymous

easy peasy

2. anonymous

if you let x be one side, then 32-x is the other side

3. anonymous

ops, sorry not 32-x it is actually 64/x

4. anonymous

then the midpoint of one side will be located at 32/x units from the other corner

5. anonymous

so using the Pythagorean theorem, we can see that $x^2 + ({32 \over x})^2$ is the length of the rope

6. anonymous

so what you want to do is to minimize this length

7. anonymous

once you take the derivative of this function and let it = 0, you should find an x that minimize it.

8. anonymous

does that help ?

9. radar

Something seems askew with this solution. $x ^{2}+(32x ^{-1})^{2}$being equal to the length as stated above does not seem complete. Wouldn't that be in a radical other the square root of that be the length of the rope??

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