document.write( "Question 1196827: A right triangle has a hypotenuse of 1. One leg is x. The other leg is (x - 7).
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Algebra.Com's Answer #829840 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "A right triangle has a hypotenuse of 1. One leg is x. The other leg is (x - 7).
\n" ); document.write( "Find the area of the triangle.
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\n" ); document.write( "\n" ); document.write( "Such a triangle does not exist.\r
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\n" ); document.write( "\n" ); document.write( "Proof:   the difference of two sides, x and x-7, must be less than the third side (from the triangle's inequality).\r
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\n" ); document.write( "\n" ); document.write( "            But the difference of the sides x and (x-7) is 7, while the third side is 1.\r
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\n" ); document.write( "\n" ); document.write( "            Contradiction.\r
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\n" ); document.write( "\n" ); document.write( "As it is worded, printed and posted, this \"problem \" is dead just from the very moment of its creation.\r
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\n" ); document.write( "\n" ); document.write( "Comment from student : You are right. It was a typo. Here it is:
\n" ); document.write( "Hypotenuse = x + 1 One side = x Other side = x - 7 Find the area.\r
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\n" ); document.write( "\n" ); document.write( "My response : It is just another story. See my solution below.\r
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document.write( "Write the Pythagorean equation\r\n" );
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document.write( "    x^2 + (x-7)^2 = (x+1)^2.\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    x^2 + (x^2 - 14x + 49) = x^2 + 2x + 1\r\n" );
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document.write( "    x^2 - 16x + 48 = 0\r\n" );
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document.write( "    (x-4)*(x-12) = 0.\r\n" );
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document.write( "For x, we have two roots:  x= 4  and  x= 12.\r\n" );
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document.write( "The root x= 4 is not the solution, since then  x-7  is negative.\r\n" );
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document.write( "The root x= 12 produces the right angled triangle (5,12,13).\r\n" );
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document.write( "Its area is   = 5*6 = 30 square units.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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