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Math Help - solving triangles

  1. #1
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    solving triangles

    The hypotenuse of a right triangle is 8 more than the shorter leg. The longer leg is 4 more than the shorter leg. Find the length of the shorter leg.


    i know your supposed to set up the equation like:

    (x+8)^2 = x^2 + (x+4)^2 and then solve for x

    however, i keep getting that x = sqrt(48)..which is wrong.
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  2. #2
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    Quote Originally Posted by samtheman17 View Post
    The hypotenuse of a right triangle is 8 more than the shorter leg. The longer leg is 4 more than the shorter leg. Find the length of the shorter leg.


    i know your supposed to set up the equation like:

    (x+8)^2 = x^2 + (x+4)^2 and then solve for x

    however, i keep getting that x = sqrt(48)..which is wrong.
    your equation is correct ... show how you calculated x = \sqrt{48}
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  3. #3
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    Quote Originally Posted by samtheman17 View Post
    The hypotenuse of a right triangle is 8 more than the shorter leg. The longer leg is 4 more than the shorter leg. Find the length of the shorter leg.

    i know your supposed to set up the equation like:

    (x+8)^2 = x^2 + (x+4)^2 and then solve for x

    however, i keep getting that x = sqrt(48)..which is wrong.
    The set up is correct.
    Go ahead & expand the expressions and simplify.
    You will get a simple quadratic expression.
    Show your work & we'll see where the differences occur.

    .
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  4. #4
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    well when i expand and simplify i get x^2 - 48 = 0

    therefore, x^2 = 48 and x = sqrt(48)
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  5. #5
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    Quote Originally Posted by samtheman17 View Post
    well when i expand and simplify i get x^2 - 48 = 0

    therefore, x^2 = 48 and x = sqrt(48)
    show your expansion ...
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  6. #6
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    x^2 + (x+4)^2 = (x+8)^2

    => X^2 +x^2 + 16 = x^2 + 64

    => x^2 + 16 = 64

    => x^2 = 48

    => x = sqrt(48)
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  7. #7
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    Quote Originally Posted by samtheman17 View Post
    x^2 + (x+4)^2 = (x+8)^2

    => X^2 + x^2 + 16 = x^2 + 64 here are your mistakes

    => x^2 + 16 = 64

    => x^2 = 48

    => x = sqrt(48)
    (x+4)^2 \ne x^2 + 16 and (x+8)^2 \ne x^2 + 64

    this is the pattern for squaring a binomial ...

    (a+b)^2 = a^2 + 2ab + b^2


    try again.
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  8. #8
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    ahhh
    thank you so much, i finally figured it out
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