Question 1180394
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The perimeter of a triangle is 30 inches. The length of the shortest side is 1/3 the length of the hypotenuse, 
and 0.5 times the length of the remaining side. What is the length of the shortest side?
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<pre>
Let x be the shortest side (the shortest leg) length.


Then the other leg is 2x, and the hypotenuse is 3x.


The Pythagoras equation is then


    x^2 + (2x)^2 = (3x)^2,   or


    x^2 + 4x^2 = 9x^2,   or


       5x^2 = 9x^2,   or

       5 = 9,  


which NEVER may happen.


The <U>ANSWER</U>  and the <U>DIAGNOSIS</U> are:


    such a triangle DOES NOR EXIST.
</pre>

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