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forty-two

  • 2 years ago

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?

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  1. mathstudent55
    • 2 years ago
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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

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

  3. forty-two
    • 2 years ago
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    @mathstudent55

  4. mathstudent55
    • 2 years ago
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    yes, distribute

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

  6. mathstudent55
    • 2 years ago
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    It looks good to me.

  7. mathstudent55
    • 2 years ago
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    Now try to factor the right side.

  8. forty-two
    • 2 years ago
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    can you help me with that, im not sure how

  9. mathstudent55
    • 2 years ago
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    First, divide both sides by 2

  10. mathstudent55
    • 2 years ago
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    also, switch sides

  11. mathstudent55
    • 2 years ago
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    2w^2 - 4w - 170 = 0 Divide both sides by 2

  12. forty-two
    • 2 years ago
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    okay so 2w^2-4w-170=0 w^2-2w-85=0?

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

  14. mathstudent55
    • 2 years ago
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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

  15. mathstudent55
    • 2 years ago
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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.

  16. mathstudent55
    • 2 years ago
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    |dw:1356497065032:dw|

  17. mathstudent55
    • 2 years ago
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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.

  18. mathstudent55
    • 2 years ago
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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.

  19. mathstudent55
    • 2 years ago
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    |dw:1356497319940:dw|

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

  21. Raja99
    • 2 years ago
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    longest ans!

  22. mathstudent55
    • 2 years ago
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    |dw:1356498098987:dw|

  23. forty-two
    • 2 years ago
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    i know, Im so sorry for mathstudent55

  24. mathstudent55
    • 2 years ago
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    Don't be sorry. this is fun for me.

  25. forty-two
    • 2 years ago
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    Okay :) thank you so much that was a lot of help

  26. mathstudent55
    • 2 years ago
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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)

  27. forty-two
    • 2 years ago
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    okay, thank you sooooo much

  28. mathstudent55
    • 2 years ago
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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)

  29. mathstudent55
    • 2 years ago
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    You're welcome.

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