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the hypotenuse of a right triangle is 3 less than 4 times the shortest leg. if the longest leg is 24cm, how long is the hypotenuse

  • math -

    Some basics:
    24 = longest leg
    x = shortest leg
    4x - 3 = hypotenuse

    Remember the following:
    a^2 + b^2 = c^2

    24^2 + x^2 = (4x - 3)^2

    576 + x^2 = 16x^2 - 24x + 9

    Set the equation equal to 0:

    0 = 15x^2 - 24x - 567

    Factoring:

    0 = 3(5x^2 - 8x - 189)

    0 = 3(5x + 27)(x - 7)

    Set the factors equal to 0:

    5x + 27 = 0; x = -27/5
    x - 7 = 0; x = 7

    Since you can't have a negative number, x = 7 is your only answer.

    I hope this explanation will help with other problems of this type.

  • math -

    Remember to substitute 7 for x to figure out the length of the hypotenuse!

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