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Math Help - Pythagorean formula question of sorts with B related to length of A

  1. #1
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    Pythagorean formula question of sorts with B related to length of A

    I am a non-math person with a math question. Suppose you have an Pythagorean formula, but there is a known relationship in length between A and B. So:

    Given that A = A and B = (0.75A) . . . your formula is:

    A(squared) + 0.75A(squared) = 361 or 19(squared)

    Can you solve this, since you now only have one unknown, A? and if so, could you show me the steps to get there? Thanks, D
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  2. #2
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    Re: Pythagorean formula question of sorts with B related to length of A

    A^2+\left(\frac{3}{4}A \right)^2=19^2

    A^2\left(1+\frac{9}{16} \right)=19^2

    \frac{25}{16}A^2=19^2

    A^2=\left(\frac{4}{5}\cdot19 \right)^2=\left(\frac{76}{5} \right)^2

    Assuming 0<A we have:

    A=\frac{76}{5}
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    Re: Pythagorean formula question of sorts with B related to length of A

    Thanks Mark. I don't follow how you got from the first line (which is just restating my question) to the second, which includes (1 + 9/16). Where the heck did the 1 come from? But actually, the final equation works and can be used with other numbers, so understanding step two is only a curiousity for me now. David

    Quote Originally Posted by MarkFL2 View Post
    A^2+\left(\frac{3}{4}A \right)^2=19^2

    A^2\left(1+\frac{9}{16} \right)=19^2

    \frac{25}{16}A^2=19^2

    A^2=\left(\frac{4}{5}\cdot19 \right)^2=\left(\frac{76}{5} \right)^2

    Assuming 0<A we have:

    A=\frac{76}{5}
    Last edited by freedda; November 2nd 2012 at 07:07 PM.
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    MHF Contributor MarkFL's Avatar
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    Re: Pythagorean formula question of sorts with B related to length of A

    Both terms on the left side have A^2 as a factor, perhaps if you put this in between the first and second lines:

    A^2\cdot1+A^2\cdot\frac{9}{16}=19^2

    It is more clear now that when we factor out the A^2 we get the second line of my first post.
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    Re: Pythagorean formula question of sorts with B related to length of A

    Mark, I don't really get it, but that's okay, since it works.

    If I was to use another fraction to multiply A by, for example B = 5/8A, I assume that I could still use your formula, only the second step would be:

    Asq (1 + 25/64) = C sq

    Is that correct? I get this by squaring each number of the fraction 5/8 which gives me the 25/64. I assume that's what you do to get to the fraction in the second step, but that's only a guess. Thanks again, David.
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Pythagorean formula question of sorts with B related to length of A

    Yes, that's correct.
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