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Math Help - tough question

  1. #1
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    tough question

    this question is particularly tough as don't know how to draw boxes and label them etc but i think it might be able to be done without seeing the boxes, here it is-

    a pen is built onto an existing rectangular building where AF is 10 units and FE is 5 units. AF and FE are shared sides between the pen and the rectangular building. the perimeter ABCDE (F is the corner of the rectangular building) is 65 units. find a relationship between x and y where AB = x and DE = y

    show that the area enclosed by the pen is 125 + 30x - x^2
    by completing the square, find the greatest possible area enclosed by the pen.

    hats off to anyone that can do this without the visual aid
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  2. #2
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    Either learn to post diagrams (or explain CLEARLY)
    else don't post anything! All you're doing is creating headaches

    For this one, as explanation, we'd need something clear, like:
    ABCD are the corners of a rectangular building.
    E is on AB, F is on AD, forming triangular pen AEF.
    AE = 10 and AF = 5........ Gey my drift?
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  3. #3
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    i think my best bet here is learning how to make a diagram, any tips on how to do that?
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by mark View Post
    this question is particularly tough as don't know how to draw boxes and label them etc but i think it might be able to be done without seeing the boxes, here it is-

    a pen is built onto an existing rectangular building where AF is 10 units and FE is 5 units. AF and FE are shared sides between the pen and the rectangular building. the perimeter ABCDE (F is the corner of the rectangular building) is 65 units. find a relationship between x and y where AB = x and DE = y

    show that the area enclosed by the pen is 125 + 30x - x^2
    by completing the square, find the greatest possible area enclosed by the pen.

    hats off to anyone that can do this without the visual aid
    Hi mark,

    Go into Start - Program - Accessories - Paint

    Create a drawing using the tools provided, labeling all parts.

    Save the drawing as a .jpg or .png file.

    Attach drawing to your post.
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  5. #5
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    ok this is gonna take a while so i might have to wait till tomorrow in that case, i'll post it here then, thanks for the advice though
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  6. #6
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    Quote Originally Posted by mark View Post
    this question is particularly tough as don't know how to draw boxes and label them etc but i think it might be able to be done without seeing the boxes, here it is-

    a pen is built onto an existing rectangular building where AF is 10 units and FE is 5 units. AF and FE are shared sides between the pen and the rectangular building. the perimeter ABCDE (F is the corner of the rectangular building) is 65 units. find a relationship between x and y where AB = x and DE = y

    show that the area enclosed by the pen is 125 + 30x - x^2
    by completing the square, find the greatest possible area enclosed by the pen.

    hats off to anyone that can do this without the visual aid

    I was able to solve the problem without a visual aid,
    but to understand my answer,
    you need to see the attached image.

    THE CONDITIONS MET:
    1) a pen is built onto an existing rectangular building (you meant ON TOP)

    2) where AF is 10 units and FE is 5 units. AF and FE are shared sides between the pen and the rectangular building.
    see image

    3) the perimeter ABCDE (F is the corner of the rectangular building) is 65 units.
    see image

    4) find a relationship between x and y where AB = x and DE = y
    this is easy
     y = \dfrac{10}{15} x

    5) show that the area enclosed by the pen is 125 + 30x - x^2
    that's what the image is for: show

    6) by completing the square, (you meant rectangle )

    7) find the greatest possible area enclosed by the pen.
    when x=15, the maximum area is 350 square units


    .
    hats off to anyone that can do this without the visual aid
    Attached Thumbnails Attached Thumbnails tough question-onto0001.jpg  
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  7. #7
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    it seems as though you've got the right answers, so well done, i take my hat off to you. still don't think i follow though, that drawing isn't like the one in the picture here. i'm gonna try to draw one now so you can see what you you can make of it
    Last edited by mr fantastic; September 3rd 2009 at 06:26 PM. Reason: Corrected a spelling error that might be misinterpreted.
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  8. #8
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    here's the question again (as it reads exactly from the book): a pen is built onto an existing rectangular building (shaded) where AF is 10 units and FE is 5 units, as shown in the diagram. the perimeter ABCDE is 65 units. find a relationship between x and y, where AB = x and DE = y

    show that the area enclosed by the pen is 125 + 30x - x^2

    by completing the square, find the greatest possible area enclosed by the pen
    Attached Thumbnails Attached Thumbnails tough question-pen.bmp  
    Last edited by mark; September 3rd 2009 at 02:19 PM.
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  9. #9
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    could someone please show me (using the post above) how exactly you would arrive at x = 15 and y = 10 and also run through how you would show that the area enclosed by the pen is 125 + 30x - x^2

    thankyou
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  10. #10
    Super Member 11rdc11's Avatar
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    First make an equation for the perimeter.

    (x+5) + (y+10) + x + y =65

    and the solve for y

    y = -x +25

    Now make and equation for the area

    A = (5+x)(10+y) -50

    A= xy +10x +5y

    Now sub y into your area equation and you have your answer.

    Hope that helps
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  11. #11
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    hi,

    i sort of understand the first bit, with making an equation for the perimeter (i'm guessing the second x and y are the two unnamed sides) but the rest i haven' got a clue about. could you tell me step by step where you get y = -x + 25 from and all the rest of it becase as usual i haven't got a clue.

    thanks
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  12. #12
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    Quote Originally Posted by 11rdc11 View Post
    First make an equation for the perimeter.

    (x+5) + (y+10) + x + y =65 .... (1)

    and the solve for y

    y = -x +25

    Now make and equation for the area

    A = (5+x)(10+y) -50

    A= xy +10x +5y

    Now sub y into your area equation and you have your answer.

    Hope that helps
    Quote Originally Posted by mark View Post
    hi,

    i sort of understand the first bit, with making an equation for the perimeter (i'm guessing the second x and y are the two unnamed sides) but the rest i haven' got a clue about. could you tell me step by step where you get y = -x + 25 from Mr F says: Make y the subject in equation (1). (The second line tells you to do this).

    and all the rest of it becase as usual i haven't got a clue.

    thanks
    The reply you got is very clear. Please review it again.


    Edit: (x+5) + (y+10) + x + y = 65 \Rightarrow 2x + 2y + 15 = 65 \Rightarrow 2x + 2y = 50 \Rightarrow x + y = 25 \Rightarrow y = 25 - x.
    Last edited by mr fantastic; September 4th 2009 at 06:13 AM.
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  13. #13
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    Mark, if your teacher's intent was to teach solving by substitution,
    then I'm perplexed by the fact that this "confusing pen on rectangle"
    was used...WHY?

    Problem could be worded simply:
    Given that x + y = 25 and A = 10x + 5y + xy, what is A in terms of x?

    Once students have learned the HOW, then bring in ye olde "word problems".
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  14. #14
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    me not having a teacher might have something to do with it. i'm just trying to learn from a book, going through all the questions one by one. i still don't understand this question or how 11rdc11 came up with those answers
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  15. #15
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    ah, i've just seen something written by mr fantastic thats helped a bit, i should have realised that first bit for myself, with or without being taught by anyone actually, those brackets 11rcd11 used threw me off
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