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Math Help - writing inequalities

  1. #1
    Junior Member Melancholy's Avatar
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    writing inequalities

    Write an inequality to describe the possible values of x.



    Help please thank you?
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    Easy, just use the Pythagorean theorem. It states that for a right triangle, two legs both squared and summed equals the hypotenuse squared. A wider angle makes way to a longer hypotenuse, so our theorem is adjusted:

    a^2+b^2 \le c^2

    We then have...

    (5x+3)^2 + 25x^2 \le c^2

    and...

    (3x+17)^2 + 25x^2 \le c^2

    BTW, I don't understand from the drawing how two sides are equal (5x)? Nevertheless, I will continue with the algebra.

    (5x+3)^2 + 25x^2 = (3x+17)^2 + 25x^2
    5x+3=3x+17
    2x=14
    x=14
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  3. #3
    Junior Member Melancholy's Avatar
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    Thank you, and the drawing is not drawn to scale, not even the one given to me originally was drawn to scale...

    I think it is supposed to be one of the "0 < x < 4" thingies though...
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  4. #4
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Melancholy View Post
    Write an inequality to describe the possible values of x.



    Help please thank you?
    note that for any triangle, the sum of the two sides is always greater than the third side and the absolute difference of the two sides is less than the third.. also, the measure of angle is proportional to the length of the sides, that is, if angle A is greater than angle B, then the side opposite angle A must be longer than the side opposite angle B..

    note, that there was a 90^o and was divided into 60^o and 30^o.. so, 30 + 95 = 125 subtracted from 180 gives 55.. thus, 3x + 17 > 5x, which implies 2x < 17 or x < 8.5

    for the lower bound, we have x cannot be non-positive, otherwise, we would have a negative o zero length given by 5x.. thus, we can assume that 0 < x < 8.5
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