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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. Yuki
    • 5 years ago
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    easy peasy

  2. Yuki
    • 5 years ago
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    if you let x be one side, then 32-x is the other side

  3. Yuki
    • 5 years ago
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    ops, sorry not 32-x it is actually 64/x

  4. Yuki
    • 5 years ago
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    then the midpoint of one side will be located at 32/x units from the other corner

  5. Yuki
    • 5 years ago
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    so using the Pythagorean theorem, we can see that \[x^2 + ({32 \over x})^2 \] is the length of the rope

  6. Yuki
    • 5 years ago
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    so what you want to do is to minimize this length

  7. Yuki
    • 5 years ago
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    once you take the derivative of this function and let it = 0, you should find an x that minimize it.

  8. Yuki
    • 5 years ago
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    does that help ?

  9. radar
    • 5 years ago
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    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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