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anonymous

  • one year ago

the length of a rectangle is 12m. lass than three times the width. the perimeter is 52cm. find the length of the rectangle

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  1. anonymous
    • one year ago
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    @mathstudent55

  2. anonymous
    • one year ago
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    @misty1212

  3. mathstudent55
    • one year ago
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    Let the width = w Then the length is 3w - 12 Ok so far?

  4. anonymous
    • one year ago
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    yes

  5. mathstudent55
    • one year ago
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    |dw:1439866523893:dw|

  6. mathstudent55
    • one year ago
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    There are two lengths with length 3w - 12, and two widths with length w. Can you find the perimeter adding the lengths and the widths?

  7. anonymous
    • one year ago
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    9w?

  8. mathstudent55
    • one year ago
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    No. Don't combine anything together. Just write all the lengths and widths that you added together on a line.

  9. anonymous
    • one year ago
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    3w-12+3 +3w-12 +w?

  10. mathstudent55
    • one year ago
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    |dw:1439866883780:dw| The two circled vertical sides are 3w - 12 + 3w - 12 The other two sides are w + w When you put it all together, you get: 3w - 12 + 3w - 12 + w + w Ok?

  11. anonymous
    • one year ago
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    yea that makes more sense.

  12. mathstudent55
    • one year ago
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    When you add the lengths of all sides, you get the perimeter. That expression we just got is the perimeter of the rectangle. We are told the perimeter is 52, so we set the expression for the perimeter equal to 52: 3w - 12 + 3w - 12 + w + w = 52

  13. mathstudent55
    • one year ago
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    That is the equation we get. It is a linear equation in one single variable, w. We can solve for w.

  14. mathstudent55
    • one year ago
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    \(3w - 12 + 3w - 12 + w + w = 52 \) We will solve it like we did before. Step 1. Combine like terms on both sides. In this case, there are like terms only on the left side, so let's work on the left side.

  15. mathstudent55
    • one year ago
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    Add all terms in w: 3w + 3w + w + w Add all numbers: -12 - 12

  16. mathstudent55
    • one year ago
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    What do you get for the sum of the terms in w?

  17. anonymous
    • one year ago
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    -24

  18. anonymous
    • one year ago
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    no sorry just 24

  19. mathstudent55
    • one year ago
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    The terms in w are in red. The plain numbers are in green. \(\color{red}{3w} \color{green}{- 12} + \color{red}{3w} \color{green}{- 12} + \color{red}{w} + \color{red}{w} = 52\) \(\color{red}{3w + 3w + w + w} \color{green}{-12 - 12} = 52\) \(\color{red}{8w } \color{green}{-24} = 52\)

  20. mathstudent55
    • one year ago
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    3w + 3w + w + w = 8w -12 -12 = -24

  21. mathstudent55
    • one year ago
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    Ok, now we have \(8w - 24 = 52\) Step 2. Now we are ready for the next step. We need to move the number, -24, to the right side. To do that, we add 24 to both sides.

  22. mathstudent55
    • one year ago
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    8w - 24 = 52 +24 +24 -------------- 8w = 76 Ok so far?

  23. anonymous
    • one year ago
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    right.

  24. mathstudent55
    • one year ago
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    For the final step, divide both sides by 8. You get w, the width. Then multiply w by 3 and subtract 12 to find the length.

  25. anonymous
    • one year ago
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    THANKS. :)

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