document.write( "Question 1136192: Rectangular flower bed 30 yards long by 24 yards wide has a walk of uniform width around it if the area of the path is 1/4 that of the flower bad, find the width of the path pls help me \n" ); document.write( "
Algebra.Com's Answer #753959 by ikleyn(52781)\"\" \"About 
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document.write( "The area of the flower bed is 30*24 = 720 square yards.\r\n" );
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document.write( "1/4 of it is  \"720%2F4\" = 180 square yards.\r\n" );
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document.write( "Let x be the uniform width of the walkway around the flower bed.\r\n" );
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document.write( "Then the outer dimensions of the larger rectangle are (30+2x) and (24+2x) yards,\r\n" );
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document.write( "so the area of the larger rectangle is  (30+2x)*(24+2x).\r\n" );
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document.write( "From the condition, we are given that\r\n" );
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document.write( "    (30+2x)*(24+2x) - 30*24 = 180   (it is exactly the area of the path !)\r\n" );
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document.write( "Simplify \r\n" );
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document.write( "    30*24 + 48x + 60x + 4x^2 - 30*24 = 180,\r\n" );
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document.write( "    4x^2 + 108x - 180 = 0,\r\n" );
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document.write( "    x^2  +  27x  - 45 = 0.\r\n" );
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document.write( "    \"x%5B1%2C2%5D\" = \"%28-27+%2B-+sqrt%28%28-27%29%5E2+%2B+4%2A45%29%29%2F2\" = \"%28-27+%2B-+sqrt%28909%29%29%2F2\" = \"%28-27+%2B-+30.15%29%2F2\".\r\n" );
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document.write( "Of the two roots, choose the positive x = \"%28-27+%2B+30.15%29%2F2\" = 1.57, \r\n" );
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document.write( "since only positive root makes sense.\r\n" );
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document.write( "ANSWER.  The walkway's uniform width is  1.57 yards.\r\n" );
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document.write( "CHECK.   (30+2*1.57)*(24+2*1.57) - 30*24 = 179.4 square yards.\r\n" );
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document.write( "          Taking rounding into account, it is good solution.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is one of many typical problems of this kind.\r
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document.write( "    From my solution, you need to learn TWO things:\r\n" );
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document.write( "        1)  The outer dimensions of the larger rectangle are 2x enlarged dimensions of the base rectangle, and\r\n" );
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document.write( "        2)  Learn how to create the base equation to find the unknown \"x\".\r\n" );
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document.write( "     The rest is just a technique.\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( "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 lessons are 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
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\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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