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anonymous

  • 5 years ago

perimeter of rectangle = 34 length of diagonal = 13 width = x derive x^2 - 17x + 60 = 0 find the dimensions of the rectangle

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  1. amistre64
    • 5 years ago
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    the optimal measurements?

  2. nikvist
    • 5 years ago
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    dimensions of rectangle are 5 and 12

  3. anonymous
    • 5 years ago
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    how did you get that? :(

  4. amistre64
    • 5 years ago
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    iwas just about to say 5 and 12.... lol

  5. anonymous
    • 5 years ago
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    you're both gods to me haha

  6. amistre64
    • 5 years ago
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    the 13 diagonal means that there is only a few setups of legs to match.... it just so happens that a 5-12-13 triangle works

  7. anonymous
    • 5 years ago
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    so why is there a quadratic equation in the problem?

  8. amistre64
    • 5 years ago
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    clutter probably :) maybe its part of the next problem

  9. nikvist
    • 5 years ago
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    \[2(a+b)=34\quad,\quad\sqrt{a^2+b^2}=13\] solve this system of equations

  10. amistre64
    • 5 years ago
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    you tend to use the derivative stuff to find the max or min area of the box..... but the 13 and 34 tend to limit you already

  11. anonymous
    • 5 years ago
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    thanks to both of you, but does the quadratic equation have anything to do with the problem

  12. amistre64
    • 5 years ago
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    it can.... if you dont know the limitations of the other stuff, that can help you to find a length...maybe

  13. anonymous
    • 5 years ago
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    thank you again, and nikvist too

  14. radar
    • 5 years ago
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    Here is how the \[x ^{2}-17x+60\] Came into play. Let x = dimension L The perimeter is 34. 34-2x = 2y which is the other dimension doubled 2y. Divide that by 2 getting: 17-x= width. Now use that to get the diagonal.

  15. anonymous
    • 5 years ago
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    The quadratic equation is there because you need to find the value of the width using the quadratic equation.

  16. radar
    • 5 years ago
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    \[x ^{2}+(17-x)^{2}=13^{2}=169\]

  17. radar
    • 5 years ago
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    \[x ^{2}+289-34x+x ^{2}=169\] \[2x ^{2}-34x+289=169\] \[2x ^{2}-34x+120=0\] \[x ^{2}-17x+60=0\] Did you follow

  18. radar
    • 5 years ago
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    You can factor solve it getting (x-5)(x-12)=0 x=5 and 12

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