document.write( "Question 1194005: A rectangular garden is 4 m by 12 m. It is to be surrounded by a walkway of uniform width.\r
\n" ); document.write( "\n" ); document.write( "Write a relation in standard form for the total are of the garden and walkway\r
\n" ); document.write( "\n" ); document.write( "I figured that out to be A=4x^2 +32x+48\r
\n" ); document.write( "\n" ); document.write( "This is the part I don't get, Stones for the walkway cost $9/m^2 If the to total cost of the walkway cannot exceed $1200, what is the maximum allowable width of the walkway? Thank you \n" ); document.write( "

Algebra.Com's Answer #826092 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A rectangular garden is 4 m by 12 m. It is to be surrounded by a walkway of uniform width.
\n" ); document.write( "Write a relation in standard form for the total are of the garden and walkway
\n" ); document.write( "I figured that out to be A=4x^2 +32x+48
\n" ); document.write( "This is the part I don't get, Stones for the walkway cost $9/m^2
\n" ); document.write( "If the to total cost of the walkway cannot exceed $1200, what is the maximum allowable width of the walkway?
\n" ); document.write( "Thank you
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document.write( "Let x be the width of the walkway, in meters.\r\n" );
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document.write( "The total area of the garden surrounded by the walkway is\r\n" );
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document.write( "    (4+2x)*(12+2x) = 4x^2 + 32x + 48 square meters.\r\n" );
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document.write( "It is what you get in your post.\r\n" );
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document.write( "To get the area of the walkway, you should subtract 4*12 = 48 square meters from it, which is the area of the garden.\r\n" );
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document.write( "You will get then  \r\n" );
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document.write( "    (4x^2 + 32x + 48) - 48 = 4x^2 + 3x  square meters, the area of the walkway.\r\n" );
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document.write( "The cost of the stone is  9*(4x^2+3x) = 36x^2 + 27x  dollars.\r\n" );
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document.write( "It should be less than or equal to 1200  dollars\r\n" );
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document.write( "     36x^2 + 27x <= 1200,\r\n" );
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document.write( "or\r\n" );
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document.write( "    12x^2 + 9x <= 400\r\n" );
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document.write( "    12x^2 + 9x - 400 <= 0.\r\n" );
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document.write( "The roots of the quadratic function on the left are 5.41 and -6.16  (approximately), obtained with the quadratic formula.\r\n" );
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document.write( "So, the maximum walkway width is about 5.41 meter.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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