document.write( "Question 1171007: A farmer has a 40 ft by 100 ft rectangular field that he wants to reduce to 67.5% of its original size. How wide of a strip should he cut around the edge of his field to do this? \n" ); document.write( "

Algebra.Com's Answer #795932 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The reduced area (the area after reducing) is 40*100*0.675 = 2700  square feet.\r\n" );
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document.write( "Let x be the uniform width of the strip to cut it around the edge of the field.\r\n" );
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document.write( "Then the new dimensions are  (100-2x) feet  and  (40-2x) feet,  and the area equation is\r\n" );
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document.write( "    (100-2x)*(40-2x) = 2700  square feet.\r\n" );
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document.write( "Now, the formal way is to reduce it to the standard form quadratic equation\r\n" );
document.write( "and then solve it using the quadratic formula or factoring.\r\n" );
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document.write( "But you may notice that  2700 = 90*30,\r\n" );
document.write( "so all you need is to subtract 10 from 100 and 40.\r\n" );
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document.write( "In other words, you mentally guess (with my help) that 2x = 10 feet;  hence  x= 5 feet  is the solution and the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus the problem is just solved and the answer is   \"the strip width is 5 feet\".\r
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\n" ); document.write( "\n" ); document.write( "        From my solution, learn two ways to solve the problem: formal algebraic solving via quadratic equation\r
\n" ); document.write( "\n" ); document.write( "        and simple way solving it mentally.
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Problems on the area and the dimensions of a rectangle surrounded by a strip\r
\n" ); document.write( "\n" ); document.write( "    - Cynthia Besch wants to buy a rug for a room \r
\n" ); document.write( "\n" ); document.write( "    - Problems on a circular pool and a walkway around it\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Dimensions and the area of rectangles and circles and their elements\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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