document.write( "Question 1041173: the hypotenuse of a right triangle is 12 inches and the area is 24 square inches. Find the dimension of the triangle, correct to one decimal place. \n" ); document.write( "

Algebra.Com's Answer #656125 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "The hypotenuse of a right triangle is 12 inches and the area is 24 square inches.
\n" ); document.write( "Find the dimension of the triangle, correct to one decimal place.
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document.write( " = ,       (1)\r\n" );
document.write( "  = ,       (2)\r\n" );
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document.write( "or\r\n" );
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document.write( " = ,        (1')\r\n" );
document.write( "     = .         (2')\r\n" );
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document.write( "Multiply eqn. (2') by 2 and add to eqn(1') (both sides). You will get\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "Thus from (1) and (2) we got \r\n" );
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document.write( "x + y = ,         (3)\r\n" );
document.write( "xy    = 48.             (4)\r\n" );
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document.write( "   Notice that in this way we decreased the degree of the original equations/system.\r\n" );
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document.write( "   It makes it easier to work in future with (3),(4) instead of (1),(2).\r\n" );
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document.write( "Next, from (3)  x = . Substitute it into (4) and get\r\n" );
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document.write( " = .     (5)\r\n" );
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document.write( " = ,\r\n" );
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document.write( "Solve this quadratic equation by applying the quadratic formula. You will get\r\n" );
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document.write( " =  =  = .\r\n" );
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document.write( "Then  =  - .\r\n" );
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document.write( "Answer. There are two solutions:\r\n" );
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document.write( "        a)  x = ,  y = ,  and\r\n" );
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document.write( "        b)  x = ,  y = .\r\n" );
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document.write( "Check.  a)  =  = 144,  xy = 4*15 - 4*3 = 60 - 12 = 48.   OK ! ! !\r\n" );
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