document.write( "Question 1204789: Find the perimeter of a right triangle whose hypotenuse is 2 and whose area is 1. \n" ); document.write( "

Algebra.Com's Answer #841293 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the perimeter of a right triangle whose hypotenuse is 2 and whose area is 1.
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document.write( "Let x and y be the legs.\r\n" );
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document.write( "Then we have \r\n" );
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document.write( "    x^2 + y^ 2 = 4     (1)    (Pythagorean equation)\r\n" );
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document.write( "       xy      = 2     (2)    (from the area equation)\r\n" );
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document.write( "Multiply equation (2) by 2 and subtract if from equation (1).  Then you get\r\n" );
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document.write( "    x^2 - 2xy + y^2 = 0,\r\n" );
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document.write( "or\r\n" );
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document.write( "    (x-y)^2 = 0.\r\n" );
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document.write( "It implies x = y.\r\n" );
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document.write( "So, our triangle is isosceles right angled triangle.\r\n" );
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document.write( "Then from equation (2), we have\r\n" );
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document.write( "    x^2 = 2,\r\n" );
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document.write( "which implies x = y = .\r\n" );
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document.write( "The perimeter then is  x + y + 2 =  +  + 2 = 2 +   units.\r\n" );
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