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Math Help - is this triginometry or algebra?

  1. #1
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    Question is this triginometry or algebra?

    a rectangle has a length 2√x cm and width √x cm
    the length of the diagonal of the triangle is √45 cm

    i) find the area of the rectangle
    ii) the area of the square is twice the area of the rectangle
    find the length of a side of the square.


    for part i) i did the a^2 + 0^2 = h^2

    then in the calc. i did 2√x got 2√5 then sq it and got 10 ,...then i
    did √x got √5 then sq it and got 5 , added them and got 15 so then i did the hypotenuse thing and √45 and got 20, yeah i know you are prob wondering how i got that and to be honest so am i lol because i used a new calc. for this and when i repeated it on an older calc. of mine i got a different answer so the CORRECT answer was :


    2x=18cm^2


    part 2 was= 6cm, but i got the answer wrong for i) so i was confused
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  2. #2
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    Hello,
    You basically have got a simultaneous equation here. Im struggling to see what you have done wrong but i think its in your pythagorous, probaly in the use of brackets. See if this helps-

    Firstly the area of the rectangle is length x bredth so

    area = (2√x)(√x) = 2x

    Then using pythagorous like you said to form a second equation thus:

    Hyp^2 = Adj^2 + Opp^2

    (√45)^2 = (√x)^2 + (2√x)^2

    45 = x + 4x

    45 = 5x

    x = 9

    The area then equals 2 x 9 = 18cm2

    Hope that helps! Not sure about part i as there is no mention in the question of a square?



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  3. #3
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    ohhh now i see ... but where did u get the 2 when u multiplied it by 9?????
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  4. #4
    ADY
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    but where did u get the 2 when u multiplied it by 9?????
    ...from the original equation:

    area = (2\sqrt{x})(\sqrt{x}) = 2x
    Last edited by ADY; August 25th 2009 at 08:23 AM.
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  5. #5
    ADY
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    area = (2\sqrt{x})(\sqrt{x}) = 2x
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