document.write( "Question 1207920: A garden 7 m by 12 m will be expanded by planting a border of flowers. The border will be of the same width around the entire garden and has an area of 92 im \n" ); document.write( "

Algebra.Com's Answer #846053 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "A garden 7 m by 12 m will be expanded by planting a border of flowers.
\n" ); document.write( "The border will be of the same width around the entire garden and has an area of 92 $\"highlight%28cross%28im%29%29\"$ square meters.
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\n" ); document.write( "\n" ); document.write( " The question absents in this post, which is inaccuracy \r
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document.write( "The garden is a rectangle 7 m by 12 m. Its area is 7*12 = 84 m^2.\r\n" );
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document.write( "Let w be the uniform width of the border of flowers around the garden.\r\n" );
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document.write( "The extended garden is a rectangle of dimensions (7+2x) by (12+2x) meters.\r\n" );
document.write( "The area of the extended garden is (7+2x)*(12+2x) m^2.\r\n" );
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document.write( "The difference of these two areas is the area of the border around the garden.\r\n" );
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document.write( "So, we write this equation\r\n" );
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document.write( "    (7+2x)*(12+2x) - 84 = 92  square meters.    (1)\r\n" );
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document.write( "At this point, the setup is complete. \r\n" );
document.write( "Now our goal is to find x from this equation.    \r\n" );
document.write( "Simplify it\r\n" );
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document.write( "    84 + 24x + 14x + 4x^2 - 84 = 92.\r\n" );
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document.write( "    4x^2 + 38x - 92 = 0,\r\n" );
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document.write( "    2x^2 + 19x - 46 = 0.\r\n" );
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document.write( "Use the quadratic formula\r\n" );
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document.write( "     =  =  = .\r\n" );
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document.write( "One root is positive, the other root is negative.\r\n" );
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document.write( "Naturally, we discard the negative root and accept the positive root\r\n" );
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document.write( "    x =  =  = 2 meters.\r\n" );
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document.write( "ANSWER.  The uniform width of the border around the garden is 2 meters.\r\n" );
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document.write( "CHECK.    We check if equation (1) is correct.\r\n" );
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document.write( "          Its left side is (7+2*2)*(12+2*2) - 84 = use your calculator = 92 m^2,  \r\n" );
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document.write( "                                                   precisely as the given area of the border.\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, look into the lessons\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
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\n" ); document.write( "\n" ); document.write( "Learn the subject from there.\r
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