document.write( "Question 1103578: A rectangular field originally has dimensions 65m by 35m. Its area is reduced by removing a strip of equal width from the east and the north sides. The area of the new field is 1000 square meters. Write a quadratic equation to model this situation. Use ‘x’ for the width of the strips removed. Solve the equation to find the dimensions of the new field.
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Algebra.Com's Answer #718261 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let \"w\" be the wide of the removed strip.\r\n" );
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document.write( "Then the new dimensions of the reduced field are 65-w meters by 35-w meters.\r\n" );
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document.write( "The area of the new rectangle is  (65-w)*(35-w),  and the equation to find w is\r\n" );
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document.write( "(65-w)*(35-w) = 1000.     (*)\r\n" );
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document.write( "You can solve this equation MENTALLY by noticing that the difference of the original dimensions is 65-35 = 30 m \r\n" );
document.write( "and noticing that the difference of the reduced dimensions is the same 30 m.\r\n" );
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document.write( "So all you need is to find two factors of 1000 with the difference between them of 30,\r\n" );
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document.write( "and it is EASY: 50 and 20.\r\n" );
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document.write( "Thus  65-w = 50,  which implies  w = 65-50 = 15.\r\n" );
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document.write( "New dimensions are 65- 15 = 50 m  and  35-15 = 20 m.\r\n" );
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\n" ); document.write( "Surely, you still have an alternative approach solving the quadratic equation (*).\r
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