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anonymous

  • 5 years ago

The perimeter of a rectangle is 34 cm. Given that the diagonal is of length 13 cm. Find the dimensions of the rectangle.

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  1. anonymous
    • 5 years ago
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    I should be able to help you, despite not being a tutor here. You must be in precalculus?

  2. anonymous
    • 5 years ago
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    Yes I am currently in precalculus.

  3. anonymous
    • 5 years ago
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    Whoa, you're back

  4. anonymous
    • 5 years ago
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    Sweet, okay. First off, you can split the rectangle up into four triangles, right?

  5. anonymous
    • 5 years ago
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    Isn't it more like two? So then it becomes 2 right angle triangles where I can then use the Pythagorean Theorem?

  6. anonymous
    • 5 years ago
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    I think it's easier to use two diagonal lines, because it makes isosceles triangles

  7. anonymous
    • 5 years ago
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    No, I think you're right. NVM <_<;;

  8. anonymous
    • 5 years ago
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    You want to use the Pythagoriean theorem. Also, write out the formula for perimeter. 2l + 2a = 34

  9. anonymous
    • 5 years ago
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    a^2+l^2=13^2

  10. anonymous
    • 5 years ago
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    The trick is to use a substituion. pick either l or a , and solve for it. In this case, I'll pick L

  11. anonymous
    • 5 years ago
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    2l = 34 - 2a (I'm going to reduce this) l = 17 - a

  12. anonymous
    • 5 years ago
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    a^2+(17-a)^2=13^2

  13. anonymous
    • 5 years ago
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    which simplifies to a+(17-a)=13

  14. anonymous
    • 5 years ago
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    Yup. I don't think that's the proper way to substitute in this case. Solve for l on a^2+l^2 = 13^2

  15. anonymous
    • 5 years ago
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    In other words, get l, without a square, by itself

  16. anonymous
    • 5 years ago
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    Does that make sense?

  17. anonymous
    • 5 years ago
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    not really :(

  18. anonymous
    • 5 years ago
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    Don't worry ^^ I'm here to help

  19. anonymous
    • 5 years ago
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    okay so l^2=(13-a)^2

  20. anonymous
    • 5 years ago
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    l=(13-a)

  21. anonymous
    • 5 years ago
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    Okay. First off, let's get L^2 by itself A^2 + L^2 = 13^2 This changes to L^2 = 169 - A^2

  22. anonymous
    • 5 years ago
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    If you'll recall, L = 17 - a

  23. anonymous
    • 5 years ago
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    So, (17-a)^2 = 169 - A^2

  24. anonymous
    • 5 years ago
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    Do you remember how to foil?

  25. anonymous
    • 5 years ago
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    yes

  26. anonymous
    • 5 years ago
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    Let's foil (17-a)^2

  27. anonymous
    • 5 years ago
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    289+a^2

  28. anonymous
    • 5 years ago
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    Nope. Remember you have to multiply both the outter and inner terms

  29. anonymous
    • 5 years ago
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    17 * 17, then 17 * -a -a * 17, then -a * -a

  30. anonymous
    • 5 years ago
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    Hmm, I think I need a whiteboard O_O

  31. anonymous
    • 5 years ago
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    i get a=3.52941...

  32. anonymous
    • 5 years ago
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    *does some math (I didn't get that far yet)

  33. anonymous
    • 5 years ago
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    Hmm, that's not what I got. Let's keep going.

  34. anonymous
    • 5 years ago
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    289 - 34a - a^2 = 169 - L^2

  35. anonymous
    • 5 years ago
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    (17-a)(17-a)=-a^2-34a+289

  36. anonymous
    • 5 years ago
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    Yup

  37. anonymous
    • 5 years ago
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    We drop that into our equation, and then we need to clean up.

  38. anonymous
    • 5 years ago
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    Bring all of the terms to one side.

  39. anonymous
    • 5 years ago
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    Did I lose you? <_< (Sorry I'm a little slow, I'm tired O_O)

  40. anonymous
    • 5 years ago
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    not really

  41. anonymous
    • 5 years ago
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    Okay. (I'm trying not to do all the work for you.) Please bring all of the terms to one side of the equation, and post them. (We're close to being done)

  42. anonymous
    • 5 years ago
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    -a^2-34a+120=-l^2

  43. anonymous
    • 5 years ago
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    (erm, sorry about the -l^2. That's -a^2) (I solved for l)

  44. anonymous
    • 5 years ago
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    so -34a+120=0

  45. anonymous
    • 5 years ago
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    Also, remember that when you square a negative, it becomes positive.

  46. anonymous
    • 5 years ago
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    -34a=-120

  47. anonymous
    • 5 years ago
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    a=3.5294...

  48. anonymous
    • 5 years ago
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    So, it was a^2 - 34a +120 = -a^2 That becomes 2a^2 - 34a + 120

  49. anonymous
    • 5 years ago
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    You forgot that when you multiply a negative by a negative, it becomes positive. (Back when you foiled)

  50. anonymous
    • 5 years ago
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    yeah kinda tired >.>

  51. anonymous
    • 5 years ago
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    It's fine. It's usually a stupid mistake that kills me in math.

  52. anonymous
    • 5 years ago
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    The next step is to reduce. Always reduce whenever you can, because it makes it math easier. (I don't know about you, but I'm lazy when it comes to math:P) So, 2a^2 - 34a + 120 becomes a^2 - 17a + 120

  53. anonymous
    • 5 years ago
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    All you need to do is factor, and you'll get your answer. s. It's plural. You can use the perimeter formula thingie to double check your answer.

  54. anonymous
    • 5 years ago
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    k

  55. anonymous
    • 5 years ago
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    its decomposition...

  56. anonymous
    • 5 years ago
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    Tell what you get ^^

  57. anonymous
    • 5 years ago
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    a=5, 12

  58. anonymous
    • 5 years ago
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    (2a-24)(a-5)

  59. anonymous
    • 5 years ago
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    yeah just too tired... making too many mistakes

  60. anonymous
    • 5 years ago
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    It's fine! You're pro now! Those answers are correct. ^^ 144 + 25 = 169 If you want to impress (cough) your math teacher, you can write the answer as if a = 5, then l = 12, or if a = 12, then l = 5

  61. anonymous
    • 5 years ago
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    The reason either answer works, is because we don't know which way the rectangle is orientated. Oh, and on a funny note, I tried solving the problem with trig. (I'm in Trig right now. That's the math class after precalc) It completely... Did not work. XD Yeesh, I'm tired too. I made some mistakes.

  62. anonymous
    • 5 years ago
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    Anyway, take it easy. God bless with the rest of your homework ^^

  63. anonymous
    • 5 years ago
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    yeah you too :)

  64. anonymous
    • 5 years ago
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    Maybe if I'm lucky, someone will help with my problem. XD

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