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Math Help - Rectangular Deck

  1. #1
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    Rectangular Deck

    A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeownercannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally.

    My Work:

    I let x = different values but the same for the width and length.

    If x = 12, then width = 12 + 15 = 27 ft.

    If x = 12, then length = 12 + 20 = 32 ft.

    The 32 ft times 27 ft = 864 ft, which is close to 900 square feet but not over 900 square feet.

    However, the answer is 12.6 not 12.

    How do I get 12.6?

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeownercannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally.

    My Work:

    I let x = different values but the same for the width and length.

    If x = 12, then width = 12 + 15 = 27 ft.

    If x = 12, then length = 12 + 20 = 32 ft.

    The 32 ft times 27 ft = 864 ft, which is close to 900 square feet but not over 900 square feet.

    However, the answer is 12.6 not 12.

    How do I get 12.6?
    let x be the the number of feet we increase the length and width by, so the new length and width are (20 + x) and (15 + x) respectively

    we want (20 + x)(15 + x) = 900

    solve for x
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  3. #3
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    I have a doubt here. The question says "by the same amount". This phrase can be interpreted in two different ways:

    (1) By same amount : same increment. Example, both increase by 10 ft
    (2) By same amount : by same percentage. (The the answer differs)

    If I consider interpretation (2),

    Final_length = Initial_Length * %total_percentage
    Final_width = Initial_width * %total_percentage

    The %total_percentage = \frac{100 + percentage_ increase}{100}

    Let %total_percentage = x

    Final_width * Final_length \leq 900

    20x * 15x \leq 900
    x^2 \leq 3
    x \leq \surd{3}
    x \leq 1.73

    Therefore increase in length = (1.73*20 -25)ft = 14.6, which is also a correct answer based on my reasoning.


    You cannot work according to the answer, because in a test, you cannot anticipate the correct answer. You have to work for it.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shailen.sobhee View Post
    I have a doubt here. The question says "by the same amount". This phrase can be interpreted in two different ways:

    (1) By same amount : same increment. Example, both increase by 10 ft
    (2) By same amount : by same percentage. (The the answer differs)

    If I consider interpretation (2),

    Final_length = Initial_Length * %total_percentage
    Final_width = Initial_width * %total_percentage

    The %total_percentage = \frac{100 + percentage_ increase}{100}

    Let %total_percentage = x

    Final_width * Final_length \leq 900

    20x * 15x \leq 900
    x^2 \leq 3
    x \leq \surd{3}
    x \leq 1.73

    Therefore increase in length = (1.73*20 -25)ft = 14.6, which is also a correct answer based on my reasoning.


    You cannot work according to the answer, because in a test, you cannot anticipate the correct answer. You have to work for it.
    i think they would say "percentage" or something like that if that's what they were after. it would be strange to interpret it otherwise really, that's the language they use here
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  5. #5
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    ok

    Quote Originally Posted by Jhevon View Post
    let x be the the number of feet we increase the length and width by, so the new length and width are (20 + x) and (15 + x) respectively

    we want (20 + x)(15 + x) = 900

    solve for x
    I thank you.
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  6. #6
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    ok

    Quote Originally Posted by shailen.sobhee View Post
    I have a doubt here. The question says "by the same amount". This phrase can be interpreted in two different ways:

    (1) By same amount : same increment. Example, both increase by 10 ft
    (2) By same amount : by same percentage. (The the answer differs)

    If I consider interpretation (2),

    Final_length = Initial_Length * %total_percentage
    Final_width = Initial_width * %total_percentage

    The %total_percentage = \frac{100 + percentage_ increase}{100}

    Let %total_percentage = x

    Final_width * Final_length \leq 900

    20x * 15x \leq 900
    x^2 \leq 3
    x \leq \surd{3}
    x \leq 1.73

    Therefore increase in length = (1.73*20 -25)ft = 14.6, which is also a correct answer based on my reasoning.


    You cannot work according to the answer, because in a test, you cannot anticipate the correct answer. You have to work for it.
    I thank you for your input.
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  7. #7
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    ok

    Quote Originally Posted by Jhevon View Post
    i think they would say "percentage" or something like that if that's what they were after. it would be strange to interpret it otherwise really, that's the language they use here
    I see what you mean.
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