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forty-two Group Title

Margaret is planning a rectangular garden. Its length is 4 feet less than twice its width. Its area is 170ft^2. what are the dimensions of the garden?

  • one year ago
  • one year ago

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  1. mathstudent55 Group Title
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    The area of a rectangle is A = LW, where A = area, L = length, W = width The width is W The length is 4 feet less than twice the width twice the width = 2W four feet less than twice the width = 2W - 4 L = 2W - 4 A = LW, but A = 170, so 170 = LW L = 2W - 4 Since the second equation is already solved for L, just plug that into the first equation and solve for W. Then plug in W in the second equation and solve for L

    • one year ago
  2. forty-two Group Title
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    170=(2w-4)w once you get here do you distribute?

    • one year ago
  3. forty-two Group Title
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    @mathstudent55

    • one year ago
  4. mathstudent55 Group Title
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    yes, distribute

    • one year ago
  5. forty-two Group Title
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    170=(2w-4)w 170=2w^2-4w 0=2w^2-4w-170 I dont think im doing this right

    • one year ago
  6. mathstudent55 Group Title
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    It looks good to me.

    • one year ago
  7. mathstudent55 Group Title
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    Now try to factor the right side.

    • one year ago
  8. forty-two Group Title
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    can you help me with that, im not sure how

    • one year ago
  9. mathstudent55 Group Title
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    First, divide both sides by 2

    • one year ago
  10. mathstudent55 Group Title
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    also, switch sides

    • one year ago
  11. mathstudent55 Group Title
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    2w^2 - 4w - 170 = 0 Divide both sides by 2

    • one year ago
  12. forty-two Group Title
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    okay so 2w^2-4w-170=0 w^2-2w-85=0?

    • one year ago
  13. mathstudent55 Group Title
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    Right. Now this kind of factoring involves simply finding two numbers that multiply to -85 and add to -2

    • one year ago
  14. mathstudent55 Group Title
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    -85 = -85 x 1 -85 + 1 = -84 -85 = 85 x -1 85 - 1 = 84 -85 = -17 x 5 -17 + 5 = -12 -85 = 17 x (-5) 17 - 5 = 12

    • one year ago
  15. mathstudent55 Group Title
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    As you can see, there are no two such numbers. This cannot be factored. We now use the quadratic equation. Let's move to a drawing.

    • one year ago
  16. mathstudent55 Group Title
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    |dw:1356497065032:dw|

    • one year ago
  17. mathstudent55 Group Title
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    That is the quadratic formula. If you have an equation of the form ax^2 + bx + c = 0, you enter the coefficients a, b, and c into the quadratic formula, as shown above, and you get the solution to the equation.

    • one year ago
  18. mathstudent55 Group Title
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    In your case we are solving for w instead of x, and we have a = 1, b = -2, and c = -85.

    • one year ago
  19. mathstudent55 Group Title
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    |dw:1356497319940:dw|

    • one year ago
  20. forty-two Group Title
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    okay so is the answer w = 2SQRT(86)?

    • one year ago
  21. Raja99 Group Title
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    longest ans!

    • one year ago
  22. mathstudent55 Group Title
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    |dw:1356498098987:dw|

    • one year ago
  23. forty-two Group Title
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    i know, Im so sorry for mathstudent55

    • one year ago
  24. mathstudent55 Group Title
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    Don't be sorry. this is fun for me.

    • one year ago
  25. forty-two Group Title
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    Okay :) thank you so much that was a lot of help

    • one year ago
  26. mathstudent55 Group Title
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    I wrote x in the drawing but I meant W. Now you know that W = 1 + sqrt(86) or W = 1 - sqrt(86)

    • one year ago
  27. forty-two Group Title
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    okay, thank you sooooo much

    • one year ago
  28. mathstudent55 Group Title
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    First look at 1 - sqrt(86). It's a negative number. A width can't be negative, so discard that solution. W = 1 + sqrt(86) L = 2W - 4 = 2(1 + sqrt(86)) - 4 = 2 + 2sqrt(86) - 4 = 2sqrt(86) - 2 So final answer is: L = 2sqrt(86) - 2 W = 1 + sqrt(86)

    • one year ago
  29. mathstudent55 Group Title
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    You're welcome.

    • one year ago
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