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Math Help - The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

  1. #1
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    The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    Hi guys,

    Question: The lengths of the sides of a right angled triangle are (2x+1) cm, 6xcm and (5x+3) cm. Calculate the value of x and hence find the area of the triangle

    I tried using Pythagoras Theorem but if I were to expand the algebra given, the answers would be completely different? How should I go around to solve it?

    Thanks
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  2. #2
    Grand Panjandrum
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    Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    Quote Originally Posted by FailInMaths View Post
    Hi guys,

    Question: The lengths of the sides of a right angled triangle are (2x+1) cm, 6xcm and (5x+3) cm. Calculate the value of x and hence find the area of the triangle

    I tried using Pythagoras Theorem but if I were to expand the algebra given, the answers would be completely different? How should I go around to solve it?

    Thanks
    There are two possibilities for the hypotenuse that you need to consider the 6x and the 5x+3 these could both be the hypotenuse, 6x if x>3 and 5x+3 if x<3.

    You need to look at both of these cases.

    CB
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    Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    Quote Originally Posted by CaptainBlack View Post
    There are two possibilities for the hypotenuse that you need to consider the 6x and the 5x+3 these could both be the hypotenuse, 6x if x>3 and 5x+3 if x<3.

    You need to look at both of these cases.

    CB
    Hmm, the answer stated here is 2. Can I assume that this question is unclear? I mean, like what you said, there are 2 hypotenuse
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    MHF Contributor Siron's Avatar
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    Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    If the answer is 2 then consider like CB has said 5x+3 as the hypothenuse, that means if we use Phytagoras theorem:
    (5x+3)^2=(6x)^2+(2x+1)^2
    Solve this equation.
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    Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    Quote Originally Posted by Siron View Post
    If the answer is 2 then consider like CB has said 5x+3 as the hypothenuse, that means if we use Phytagoras theorem:
    (5x+3)^2=(6x)^2+(2x+1)^2
    Solve this equation.
    Yeah, but I think the question itself is unclear. Without the answer, how would we have know that (5x+3) is the hypotenuse
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    Grand Panjandrum
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    Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    Quote Originally Posted by FailInMaths View Post
    Yeah, but I think the question itself is unclear. Without the answer, how would we have know that (5x+3) is the hypotenuse
    By doing the calculations in both cases, you will find only one solution consistent with x>0 and x<3 for the 6x hypotenuse and x>3 for the 5x+3 hypotenuse.

    So you compute all four solutions and only one is consistent with the constraints.

    CB
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    Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

    Quote Originally Posted by CaptainBlack View Post
    By doing the calculations in both cases, you will find only one solution consistent with x>0 and x<3 for the 6x hypotenuse and x>3 for the 5x+3 hypotenuse.

    So you compute all four solutions and only one is consistent with the constraints.

    CB
    Ok, I get it now, thanks
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