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Thread: Solving by Factoring :(

  1. #1
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    Default Solving by Factoring :(

    Set up an equation and solve the problem.
    The sum of the areas of two squares is 250 square inches. Each side of the larger square is three times the length of a side of the smaller square. Find the length of a side of each square.

    Set up an equation and solve the problem.
    A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 21 inches by 6 inches, in order to reduce the size of the paper to an area of 34 square inches. Find the width of the strip.

    Help

    I really need help with these type of equations. would be nice for a description on how you did it.

    thanks

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    Side1 is 1 side of the 1st square
    Side2 is 1 side of the 2nd square

    Area of a square is Side*Side or Side^2

    (Side1 * Side1) + (Side2 * Side2) = 250
    3Side2 = Side1

    This should solve the 1st question. Plug in for Side1 and solve.

    (3Side2 * 3Side2) + (Side2)^2 = 250
    9(Side2)^2 + (Side2)^2 = 250
    10(Side2)^2 = 250
    Side2 = Sqrt(25)
    Side2 = 5

    3Side2 = Side1
    3(5) = Side1
    15 = Side1

    Check Solution:
    (15*15) + (5*5) = 250
    225 + 25
    250 = 250

    Correct

    "Failure is the opportunity to begin again more intelligently" (Henry Ford)


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    I have no idea what you are talking about

    Whats with slide 1 and slide 2?

    Do you mean it represents x?

    holy crap i understand it now thanks

    wait.. what if its the difference of 2 squares?

    The difference of the areas of two squares is 1575 square feet. Each side of the larger square is eight times the length of a side of the smaller square. Find the length of a side of each square.

    Get me started if you can, because i want to finish it. just tell me what to do..
    Last edited by Overtime; 10-20-2010 at 01:59 AM.

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    Same concepts, just a little different equations.

    (Side1 * Side1) - (Side2 * Side2) = 1575
    8Side2 = Side1

    You can get it from here

    "Failure is the opportunity to begin again more intelligently" (Henry Ford)


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    9(Side2)^2 + (Side2)^2 = 250
    10(Side2)^2 = 250

    what did you do to get 10? did you add +1?

    cuz i did the same with 8 and now i have 64

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    yes, I added 1.

    Its the same concept as 9x + x = 10x,

    or 9x^2 + x^2 = 10x^2

    "Failure is the opportunity to begin again more intelligently" (Henry Ford)


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    sl = side of larger square
    ss = side of smaller square
    8ss = sl (given)

    sl^2 - ss^2 = 1575 (using the information given)

    substituting 8ss = sl, we get:

    sl^2 - (1/8 * sl)^2 = 1575 (plugging in 8ss = sl, or ss = 1/8 * sl)

    You can find the rest below this line if you get stuck or want to check your work.

    sl^2 - 1/64 * sl^2 = 1575
    64/64 * sl^2 - 1/64 sl^2 = 1575
    63/64 * sl^2 = 1575
    sl^2 = 1600
    sl = 40 ft

    ss = 1/8 * sl
    ss = 1/8 * 40
    ss = 5 ft


    For the second one:

    l = 21 in.
    w = 6 in.
    A = l * w

    The problem says you're removing equal parts from both sides and both ends. We'll call the part you remove from one side x. Since you're removing from both sides and both parts, you're effectively removing 2x from both the length and width of the paper. Therefore, your new equation for the area looks like this:

    A = (l - 2x) * (w - 2x)
    A = (21 - 2x) * (6 - 2x)

    We know the area of the new paper is going to be 34 in^2, so we can plug that in:

    34 = (21 - 2x) * (6 - 2x)

    I'll let you figure out the rest (though I'll leave it below for you to highlight again if you get stuck):

    34 = 126 - 42x - 12x + 4x^2
    4x^2 - 54x + 126 = 34
    4x^2 - 54x + 92 = 0

    Using the quadratic formula:

    x = (54 +- sqrt((-54)^2 - 4(4)(92))) / 2(4)
    x = (54 +- sqrt(1444)) / 8
    x = (54 +- 38) / 8
    x = (54 + 38) / 8 or x = (54 - 38) / 8
    x = 11.5 or x = 2

    Since the length of the smallest side (6) is less than 11.5, we can eliminate that answer. The correct answer is 2 in.
    Last edited by Method; 10-20-2010 at 05:14 AM.
    :-)

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    thanks guys.

    Figured it out finally xD

    I got it.

    The larger was 40
    and the smaller was 5.

    40*40=1600
    5*5=25

    Subtract both.

    Bam! =1575

    for the 2nd one Method, im gettting -7/4.

    My numbers changed on me on the assigment.

    Its now 17x3 and 32 for the area
    Last edited by Overtime; 10-20-2010 at 05:20 PM.

  9. #9
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    Quote Originally Posted by Squancy View Post
    thanks guys.

    Figured it out finally xD

    I got it.

    The larger was 40
    and the smaller was 5.

    40*40=1600
    5*5=25

    Subtract both.

    Bam! =1575

    for the 2nd one Method, im gettting -7/4.

    My numbers changed on me on the assigment.

    Its now 17x3 and 32 for the area
    You can't remove a negative amount of paper, so a negative value makes no sense. You may be doing something odd in your calculations. And if the numbers change, just substitute those new numbers into the same equation:

    A = l * w
    32 = (17 - 2x) * (3 - 2x)
    32 = 51 - 34x - 6x + 4x^2
    4x^2 - 40x + 51 = 32
    4x^2 - 40x + 19 = 0

    Using the quadratic formula:

    x = (40 +- sqrt((-40)^2 - 4(4)(19))) / 2(4)
    x = (40 +- sqrt(1296)) / 8
    x = (40 +- 36) / 8
    x = (40 + 36) / 8 or x = (40 - 36) / 8
    x = 9.5 or x = 0.5

    Again, since you can't remove more paper from a side than is available, 9.5 doesn't make sense. The answer, therefore, is 0.5 inches from both sides and both parts.
    :-)

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