document.write( "Question 1096574: An engineer wants to surround a rectangular a pool with dimension 10m by 20m with a stone border of uniform width. there are enough stones to cover 64 square meters . how wode should the border be? \n" ); document.write( "

Algebra.Com's Answer #711031 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let w be the uniform width of the stone border.\r\n" );
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document.write( "Then the exterior dimensions of the larger rectangle are (10+2w) meters by (20+2w) meters, \r\n" );
document.write( "and the area of the larger rectangle is the product  (10+2w)*(20+2w) square meters.\r\n" );
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document.write( "Hence, the area of the border itself is  (10+2w)*(20+2w) - 10*20,  and it is equal exactly to  64 square meters.\r\n" );
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document.write( "It gives you an equation for w:\r\n" );
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document.write( "(10+2w)*(20+2w) - 10*20 = 64,\r\n" );
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document.write( "40w + 20w + 4w^2 = 64,\r\n" );
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document.write( "4w^2 + 60w - 64 = 0,\r\n" );
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document.write( "w^2 + 15w - 16 = 0,\r\n" );
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document.write( "(w+16)*(w-1) = 0  ====>   the only positive root  w= 1 gives you the answer to the problem's question.\r\n" );
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\n" ); document.write( "For many other similar solved problems see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Problems on the area and the dimensions of a rectangle surrounded by a strip\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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