document.write( "Question 1054977: If each dimension of a room is increased one meter, the area is increased by 51 meters ; and if the length is increased by one meter and the width diminished by one meter, the area is decreased 3 square meters. Find the dimensions \n" ); document.write( "

Algebra.Com's Answer #670193 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "If each dimension of a room is increased one meter, the area is increased by 51 meters ; and if the length is increased
\n" ); document.write( "by one meter and the width diminished by one meter, the area is decreased 3 square meters. Find the dimensions
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document.write( "(x+1)*(y+1) - xy = 51,   (1)   (x = the length,  y = the width)\r\n" );
document.write( "(x+1)*(y-1) - xy = -3.   (2)\r\n" );
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document.write( "Simplify (by opening the parentheses)\r\n" );
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document.write( "xy + x + y + 1 - xy = 51,   \r\n" );
document.write( "xy - x + y - 1 - xy = -3,\r\n" );
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document.write( "or\r\n" );
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document.write( " x + y = 50,             (1')\r\n" );
document.write( "-x + y = -2              (2')\r\n" );
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document.write( "Add (1') and (2') (both sides). You will get\r\n" );
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document.write( "2y = 48.  Then  y =  = 24.  Hence, the width is 24 m.\r\n" );
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document.write( "Then from  (1') x = 50-y = 50-24 = 26 m.\r\n" );
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document.write( "Answer.  The length is 26 m,  the width is 24 m.\r\n" );
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