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Math Help - Inscribed rectangle in triangle

  1. #1
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    Inscribed rectangle in triangle

    Hi guys,

    Need help with this one.

    1) A recangle w/ a perimetrer of 15cm is inscribed in traingle ABC. A=(0,8) B=(6,0) C is unknown. Find the dimensions of the rectangle. Ill include a picture of the diagram so it will be more clear.

    http://i58.photobucket.com/albums/g2...s/triangle.jpg < Link


    Thanks!!!
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by AndrewK View Post
    Hi guys,

    Need help with this one.

    1) A recangle w/ a perimetrer of 15cm is inscribed in traingle ABC. A=(0,8) B=(6,0) C is unknown. Find the dimensions of the rectangle. Ill include a picture of the diagram so it will be more clear.

    http://i58.photobucket.com/albums/g2...s/triangle.jpg < Link


    Thanks!!!
    Is C required to be on X-axis?
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  3. #3
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    ^ Yes it is malaygoel
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by AndrewK View Post
    Hi guys,

    Need help with this one.

    1) A recangle w/ a perimetrer of 15cm is inscribed in traingle ABC. A=(0,8) B=(6,0) C is unknown. Find the dimensions of the rectangle. Ill include a picture of the diagram so it will be more clear.

    http://i58.photobucket.com/albums/g2...s/triangle.jpg < Link


    Thanks!!!
    first let's find the equation of the line.

    what is the slope?

    m = (y2 - y1)/(x2 - x1) = (8-0)/(0-6) = -4/3

    using the point-slope form with m = -4/3 and (x1,y1) = (0,8), we get:
    y - y1 = m(x - x1)
    => y - 8 = (-4/3)x
    => y = (-4/3)x + 8

    now the rectangle goes up to the line y, that means the height of the rectangle will be given by the formula (-4/3)x + 8

    now the length of the rectangle is just x. we are told that the perimeter is 15, which is the sum of all the sides, so

    P = 15 = 2x + 2[(-4/3)x + 8]
    => 15 = 2x - (8/3)x + 16
    => 15 - 16 = -(2/3)x
    => -1 = -(2/3)x
    => x = 3/2

    but y = (-4/3)x + 8 = (-4/3)(3/2) + 8 = 6

    so the dimensions of the rectangle is length = 3/2, height = 6

    let's check this to make sure:
    P = 3/2 + 3/2 + 6 + 6 = .....drum roll please....= 15! Yay! ........that's 15, not 15 factorial

    did you understand the process?
    Last edited by Jhevon; April 24th 2007 at 07:48 AM.
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