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gabbyalicorn

  • one year ago

The width of a rectangle is 6 in. less than its length. The perimeter is 68 in. What is the width of the rectangle? in.

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  1. gabbyalicorn
    • one year ago
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    Hi pooja.

  2. pooja195
    • one year ago
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    Uh i think the answer is in the question....if im right

  3. anonymous
    • one year ago
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    divide it in two first

  4. Jhannybean
    • one year ago
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    |dw:1442028600183:dw|

  5. Jhannybean
    • one year ago
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    Omg I forgot the shapes have the "fill" option.... anyway.

  6. anonymous
    • one year ago
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    yeah

  7. gabbyalicorn
    • one year ago
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    When you say divide two first, do you mean 68 ÷ 2 and 6÷ 2

  8. anonymous
    • one year ago
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    no 68 by 2

  9. anonymous
    • one year ago
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    then subtract 6 from that

  10. gabbyalicorn
    • one year ago
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    okay, that is 34...

  11. Jhannybean
    • one year ago
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    the length of the rectangle is given, but they say the `width` `is (equal to)` the `length - 6 in`You can rewrite this as \(\sf w = L-6\)

  12. Jhannybean
    • one year ago
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    So the Perimeter of a rectangle is represented as: \[\sf P = 2L +2W\]

  13. Jhannybean
    • one year ago
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    Since we're given the perimeter, and that is = 68 in. we can substitute that in to our formula. \[\sf 68 = 2L +2W\]

  14. Jhannybean
    • one year ago
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    But we also know something else, \(\sf W=L-6\)

  15. gabbyalicorn
    • one year ago
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    68 - 6?

  16. Jhannybean
    • one year ago
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    So we can substitute this in to the formula for the perimeter. \[\sf 68 = 2L+2(L-6)\]

  17. Jhannybean
    • one year ago
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    Are you following, @gabbyalicorn ?

  18. gabbyalicorn
    • one year ago
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    Um, somewhat... I don't really get it but i'm following the steps if that's what you mean. :)

  19. Jhannybean
    • one year ago
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    Which part are you confused with? Let's clarify that before moving on.

  20. gabbyalicorn
    • one year ago
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    is L the variable we are trying to find

  21. gabbyalicorn
    • one year ago
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    the number for...

  22. Jhannybean
    • one year ago
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    We are trying to find W (width). The problem indiscreetly gives us the equation for the width by saying that the width IS 6 LESS THAN the length. We can write an equation for that. \(\sf w = L-6\)

  23. gabbyalicorn
    • one year ago
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    but what is L

  24. Jhannybean
    • one year ago
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    But we can't automatically find the width, \(\sf w\) can we? We need to find the length, \(\sf L\) first.

  25. Jhannybean
    • one year ago
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    That is where we use the equation for the perimeter of the rectangle. \(\sf P = 2L +2w\)

  26. Jhannybean
    • one year ago
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    Do you see how this works?

  27. gabbyalicorn
    • one year ago
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    I think I'm getting it...

  28. Jhannybean
    • one year ago
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    Okay, so we have \[\sf 68 = 2L+2(L-6)\] We need to first distribute (meaning multiply) 2 to each term inside the parenthesis. \[2 \cdot L =~?\]\[2\cdot (-6) =~?\]

  29. gabbyalicorn
    • one year ago
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    |dw:1442029733818:dw|

  30. Jhannybean
    • one year ago
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    Good

  31. gabbyalicorn
    • one year ago
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    :)

  32. Jhannybean
    • one year ago
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    \[\sf 68 = 2L +2L-12\]We add +12 to both sides of the equation.

  33. gabbyalicorn
    • one year ago
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    why - 12 I thought you said add

  34. Jhannybean
    • one year ago
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    because we want to isolate the L's to one side of the equation, we need to eliminate the 12 from that side. In order to eliminate it we need to add +12 to it. \[\sf +12-12 = 0\]So, \(\sf 68 + 12 =~?\)

  35. gabbyalicorn
    • one year ago
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    80

  36. Jhannybean
    • one year ago
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    So now we have \[\sf 80 = 2L + 2L\]\[\sf 2L + 2L =~?\]

  37. gabbyalicorn
    • one year ago
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    4L ?

  38. Jhannybean
    • one year ago
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    Good.

  39. gabbyalicorn
    • one year ago
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    :}

  40. Jhannybean
    • one year ago
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    \[\sf 80 = 4L\]Now we want to isolate the right side of the equation so we have JUST L. This is when we divide BOTH sides of the equation by 4. \[\sf \frac{80}{4}=~?\]

  41. gabbyalicorn
    • one year ago
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    20

  42. Jhannybean
    • one year ago
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    ALRIGHT! So now we have figured out \(\sf L\). \[\sf L=20\]Now we can go back to our equation for width and plug in L. \[\sfW=L-6\]So therefore what does W =?

  43. Jhannybean
    • one year ago
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    Sorry, typo. \(\sf W=L-6\)*

  44. gabbyalicorn
    • one year ago
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    20 - 6 = 14?

  45. Jhannybean
    • one year ago
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    That's correct :)

  46. gabbyalicorn
    • one year ago
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    Yes. :)

  47. Jhannybean
    • one year ago
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    Great! You worked it out yourself :)

  48. gabbyalicorn
    • one year ago
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    :D Thank you for helping me and not giving up on me! I reallu appreciate it. :)

  49. Jhannybean
    • one year ago
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    No problem ^^

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