document.write( "Question 248100: A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower bed? \n" ); document.write( "

Algebra.Com's Answer #181127 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.
\n" ); document.write( " The combined area of the lawn and the flower bed is 165m^2. What is the width of the flower
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\n" ); document.write( "Let x = the width of flower bed
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\n" ); document.write( "Then the overall dimensions (flower bed & lawn) will be:
\n" ); document.write( "(2x + 8) by (2x + 4)
\n" ); document.write( ":
\n" ); document.write( "Overall area
\n" ); document.write( "(2x+8)*(2x+4) = 165
\n" ); document.write( "FOIL
\n" ); document.write( "4x^2 + 8x + 16x + 32 = 165
\n" ); document.write( "A quadratic equation
\n" ); document.write( "4x^2 + 24x + 32 - 165 = 0
\n" ); document.write( "4x^2 + 24x - 132 = 0
\n" ); document.write( "Simplify, divide by 4, results:
\n" ); document.write( "x^2 + 6x - 33 = 0
\n" ); document.write( "Use the quadratic formula to solve this
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "In this problem: a=1; b=6; c=-33
\n" ); document.write( " $\"x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A-33+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( "Do the math here and you should get a positive solutions of:
\n" ); document.write( "x ~ 3.48 meters is the width of the flower bed
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\n" ); document.write( ":
\n" ); document.write( "Check on a calc: enter (2(3.48)+8)*(2(3.48)+4) = 164 ~ 165
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