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YanaSidlinskiy

  • one year ago

The area of a rectangular garden is 54 square meters. The width is 7 meters longer than one-third of the length. Find the length and the width of the garden. Use the formula, are = length * width.

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  1. jim_thompson5910
    • one year ago
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    |dw:1438819879525:dw|

  2. jim_thompson5910
    • one year ago
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    The width is 7 meters longer than one-third the length, so we can say \[\Large W = \frac{1}{3}L + 7\]

  3. jim_thompson5910
    • one year ago
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    The area of the rectangle is length * width, so \[\Large A = L*W\] \[\Large 54 = L*\left(\frac{1}{3}L + 7\right)\] Do you see how to solve for L from here?

  4. YanaSidlinskiy
    • one year ago
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    Yeah. Would it be \[54=\frac{ 1 }{ 3 }x^2+7x\] From there I need help...

  5. jim_thompson5910
    • one year ago
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    what I would do from there is multiply everything by 3 to get rid of the fraction

  6. jim_thompson5910
    • one year ago
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    then get everything to one side

  7. YanaSidlinskiy
    • one year ago
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    So like multiply 1/3x^2(3) and multiply 7x(3)?

  8. jim_thompson5910
    • one year ago
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    yeah and 54 as well

  9. YanaSidlinskiy
    • one year ago
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    Okie, one sec.

  10. YanaSidlinskiy
    • one year ago
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    Got it. Would it be: \[162=1x^2+21x\]

  11. YanaSidlinskiy
    • one year ago
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    Or instead I should just put \[x^2\]

  12. jim_thompson5910
    • one year ago
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    either works

  13. jim_thompson5910
    • one year ago
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    now move that 162 over

  14. YanaSidlinskiy
    • one year ago
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    Ok. I have a question... Does it matter with what number I multiply the numbers with?

  15. jim_thompson5910
    • one year ago
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    you mean like how you multiplied everything by 3 just now?

  16. YanaSidlinskiy
    • one year ago
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    Yeah.

  17. jim_thompson5910
    • one year ago
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    The denominator of the fraction was 3, so multiplying everything by that clears out the denominator (ie eliminates the fraction)

  18. jim_thompson5910
    • one year ago
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    if you picked another number that wasn't a multiple of 3, then the denominator or fraction wouldn't go away

  19. YanaSidlinskiy
    • one year ago
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    Oh ok! Gotcha! Ok. So I got: 1x^2+21x-162=0 Give me a sec. I wanna do it myself and you tell me what I got wrong.

  20. YanaSidlinskiy
    • one year ago
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    I got: (x+54)(x-3) PLEASE tell me it's right haha! I've had so much trouble with this today.

  21. jim_thompson5910
    • one year ago
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    54 times -3 = -162 .... true 54 plus -3 = 21 ... false so that's not the correct factorization

  22. YanaSidlinskiy
    • one year ago
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    I'm confused and I think this is the stop. So how would I know which number goes where? Or more like why does it matter where I put down the sign with which number?

  23. YanaSidlinskiy
    • one year ago
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    *spot

  24. jim_thompson5910
    • one year ago
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    The quadratic formula may be easier to work with. Did you want to use that?

  25. YanaSidlinskiy
    • one year ago
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    Yeah, I wanna use that instead... This is really hard for me and I have no idea why...

  26. YanaSidlinskiy
    • one year ago
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    Ok, let me figure it out using the quadratic formula.

  27. jim_thompson5910
    • one year ago
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    1x^2+21x-162 means a = 1 b = 21 c = -162 plug those values into \[\Large x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

  28. YanaSidlinskiy
    • one year ago
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    I'm not exactly sure if this is right, but so far I have: \[x=\frac{ -21\pm \sqrt{207} }{ 2 }\] Is that right?

  29. YanaSidlinskiy
    • one year ago
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    *-201

  30. jim_thompson5910
    • one year ago
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    The 207 portion is incorrect b^2 - 4ac = 21^2 - 4*1*(-162) = 1089

  31. YanaSidlinskiy
    • one year ago
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    So I multiplied it incorrectly? How?

  32. jim_thompson5910
    • one year ago
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    21^2 = 441 4*1*(-162) = -648

  33. jim_thompson5910
    • one year ago
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    21^2 - 4*1*(-162) = 441 - (-648) = 1089

  34. YanaSidlinskiy
    • one year ago
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    Ahh! That's what I was missing! Gotcha! Ok. Hang on:)

  35. YanaSidlinskiy
    • one year ago
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    So it'd be like \[x=\frac{ -21\pm \sqrt{1089} }{ 2 }\] ?

  36. jim_thompson5910
    • one year ago
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    correct

  37. YanaSidlinskiy
    • one year ago
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    Sorry for making you wait.... I'm kinda slow on thinking right now...

  38. jim_thompson5910
    • one year ago
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    You're doing great. Don't worry.

  39. YanaSidlinskiy
    • one year ago
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    I hope so... So my answer would be x=534?

  40. YanaSidlinskiy
    • one year ago
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    The answer can never be negative.. I know that...

  41. jim_thompson5910
    • one year ago
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    no

  42. YanaSidlinskiy
    • one year ago
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    Ughgh. Ok, I need some real help. What is it?

  43. jim_thompson5910
    • one year ago
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    \[\Large x=\frac{ -21\pm \sqrt{1089} }{ 2 }\] \[\Large x=\frac{ -21+ \sqrt{1089} }{ 2 } \ \text{ or } \ x=\frac{ -21- \sqrt{1089} }{ 2 }\] \[\Large x=\frac{ -21+ 33 }{ 2 } \ \text{ or } \ x=\frac{ -21- 33 }{ 2 }\] \[\Large x=?? \ \text{ or } \ x=??\]

  44. YanaSidlinskiy
    • one year ago
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    Wow, ok. I divided 1089 by 2 so that's what threw me off... Hang on let me get the final answer..

  45. YanaSidlinskiy
    • one year ago
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    I got 6, -27.

  46. jim_thompson5910
    • one year ago
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    x took the place of the length L so L = 6 or L = -27 but a negative length makes no sense which is why we ignore -27

  47. YanaSidlinskiy
    • one year ago
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    So, what would be my width? I don't seem to be understanding that part..

  48. jim_thompson5910
    • one year ago
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    go back to \[\Large W = \frac{1}{3}L + 7\]

  49. jim_thompson5910
    • one year ago
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    plug in L = 6

  50. jim_thompson5910
    • one year ago
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    or you can ask yourself "something times 6 gives the area of 54, what is that something?"

  51. YanaSidlinskiy
    • one year ago
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    Oh yeah. Sorry. I'm like dead tired and didn't get enough sleep lol.. 9

  52. jim_thompson5910
    • one year ago
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    yep L = 6 and W = 9

  53. YanaSidlinskiy
    • one year ago
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    Anyways, THANK YOU SO MUCH!!!!!! I can't appreciate you enough. I'd be sitting behind the computer sending you billions of messages with different thank you's. Thanks again!

  54. jim_thompson5910
    • one year ago
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    I'm glad it's making sense now

  55. YanaSidlinskiy
    • one year ago
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    Yeah, me too. I have another one similar to this, but I'll figure it out myself and let you check it since it's coming to my brain lol. Anyways, just expect a "check message" from me or something...

  56. jim_thompson5910
    • one year ago
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    ok sounds like a good plan to me

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