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Thread: Solving Pythagoras Theorem eqn a^2 + (1.3a)^2 = c^2 for "a": possible?

  1. #1

    Solving Pythagoras Theorem eqn a^2 + (1.3a)^2 = c^2 for "a": possible?

    I thought I remembered my algebra from a half century ago. I don't.
    Is it possible to solve the equation below for a? <--- CORRECTION: initial post said "c" here. That was a mistake. I meant "a"
    a^2 + (1.3a)^2 = c^2
    Why? Because I'm trying to constrain (crop) an image to have a certain number of pixels. 1.3 is the image's aspect ratio. So the Pythagorean b is equal to 1.3a

    So the above is the
    Pythagorean formula:
    Width^2 * (1.3 * Width)^2 = Total_Pixels^2
    TIA
    Last edited by tfield98; 02-11-2018 at 01:37 AM.

  2. #2
    Elite Member
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    Quote Originally Posted by tfield98 View Post
    I thought I remembered my algebra from a half century ago. I don't.
    Is it possible to solve the equation below for c?
    a^2 + (1.3a)^2 = c^2
    Why? Because I'm trying to constrain (crop) an image to have a certain number of pixels. 1.3 is the image's aspect ratio. So the Pythagorean b is equal to 1.3a

    So the above is this Pythagorean formula:

    Width^2 * (1.3 * Width)^2 = Total_Pixels^2
    TIA
    You'll need a square root.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
    Quote Originally Posted by tkhunny View Post
    You'll need a square root.
    Thanks, tkhunny.

    My mistake, I meant to say "solve for a, knowing c"

  4. #4
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    Quote Originally Posted by tfield98 View Post
    a^2 + (1.3a)^2 = c^2
    solve for a, knowing c
    Let k = 1.3; then:

    a^2 + (ka)^2 = c^2
    a^2 + k^2 * a^2 = c^2
    a^2(1 + k^2) = c^2
    a^2 = c^2 / (1 + k^2)
    a = sqrt[c^2 / (1 + k^2)]

    Try that out using (as example) k = 3 and c^2 = 250
    You'll get a = 5

    Now that you're satisfied(!), use it on your problem
    I'm just an imagination of your figment !

  5. #5

    Solving Pythagoras Theorem eqn a^2 + (1.3a)^2 = c^2 for "a": possible?

    Quote Originally Posted by Denis View Post
    Let k = 1.3; then:

    a^2 + (ka)^2 = c^2
    a^2 + k^2 * a^2 = c^2
    a^2(1 + k^2) = c^2
    a^2 = c^2 / (1 + k^2)
    a = sqrt[c^2 / (1 + k^2)]
    That's exactly what I was looking for. Thanks!!

    The algebra is straight-forward, but I couldn't have come up with it on my own.

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