document.write( "Question 390023: A rectangle field is going to be completely enclosed by 100m of fencing. Determine the dimensions of the field that will result in an area of 575m square. Round your answer to the nearest tenth of a metre. \n" ); document.write( "
Algebra.Com's Answer #276492 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
A rectangle area:\r
\n" ); document.write( "\n" ); document.write( "\"A+=+ab\"....where \"a\" and \"b\" are length and width\r
\n" ); document.write( "\n" ); document.write( "given:\r
\n" ); document.write( "\n" ); document.write( "\"A+=575m%5E2\" and \"100m\" for fencing which is equal to perimeter \"P+=+2%28a%2Bb%29\"\r
\n" ); document.write( "\n" ); document.write( "to find: \"a\" and \"b\"\r
\n" ); document.write( "\n" ); document.write( "use\r
\n" ); document.write( "\n" ); document.write( "\"ab+=575m%5E2\" and \"100m+=+2%28a%2Bb%29\" and solve the system\r
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\n" ); document.write( "\n" ); document.write( "\"ab+=575m%5E2\"...solve for \"a\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=575m%5E2%2Fb\"........substitute in \"100m+=+2%28a%2Bb%29\" and find \"b\"\r
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\n" ); document.write( "\n" ); document.write( "\"cross%28100%2950m+=+cross%282%29%28%28575m%5E2%2Fb%29%2Bb%29\" \r
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\n" ); document.write( "\n" ); document.write( "\"50m+=+%28575m%5E2%2Fb%29%2Bb\"...both sides multiply by \"b\"\r
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\n" ); document.write( "\n" ); document.write( "\"50m+%2Ab=+b%28575m%5E2%2Fb%29%2Bb%2Ab\"\r
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\n" ); document.write( "\n" ); document.write( "\"50m+%2Ab=+cross%28b%29%28575m%5E2%2Fcross%28b%29%29+%2Bb%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"50m+%2Ab=+575m%5E2+%2Bb%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"50m+%2Ab-+b%5E2=+575m%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"-+b%5E2+%2B+50m+%2Ab+-575m%5E2+=0\"...solve for \"b\"\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"-x%5E2%2B50%2Ax-575=0\" ( notice \"a=-1\", \"b=50\", and \"c=-575\")
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\n" ); document.write( " \"x+=+%28-50+%2B-+sqrt%28+%2850%29%5E2-4%2A-1%2A-575+%29%29%2F%282%2A-1%29\" Plug in a=-1, b=50, and c=-575
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\n" ); document.write( " \"x+=+%28-50+%2B-+sqrt%28+2500-4%2A-1%2A-575+%29%29%2F%282%2A-1%29\" Square 50 to get 2500
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\n" ); document.write( " \"x+=+%28-50+%2B-+sqrt%28+2500%2B-2300+%29%29%2F%282%2A-1%29\" Multiply \"-4%2A-575%2A-1\" to get \"-2300\"
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\n" ); document.write( " \"x+=+%28-50+%2B-+sqrt%28+200+%29%29%2F%282%2A-1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%28-50+%2B-+10%2Asqrt%282%29%29%2F%282%2A-1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%28-50+%2B-+10%2Asqrt%282%29%29%2F-2\" Multiply 2 and -1 to get -2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%28-50+%2B+10%2Asqrt%282%29%29%2F-2\" or \"x+=+%28-50+-+10%2Asqrt%282%29%29%2F-2\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=-50%2F-2%2B10%2Asqrt%282%29%2F-2\" or \"x=-50%2F-2-10%2Asqrt%282%29%2F-2\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=25-5%2Asqrt%282%29\" or \"x=25%2B5%2Asqrt%282%29\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=25-5%2Asqrt%282%29\" or \"x=25%2B5%2Asqrt%282%29\"
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\n" ); document.write( "\n" ); document.write( "one solution\r
\n" ); document.write( "\n" ); document.write( "\"b=25-5sqrt%282%29=25-5%2A1.41=+25-7.05=+17.95m\"\r
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\n" ); document.write( "\n" ); document.write( "\"b=+17.95m\"\r
\n" ); document.write( "\n" ); document.write( "other solution\r
\n" ); document.write( "\n" ); document.write( "\"b=25%2B5sqrt%282%29=25%2B5%2A1.41=+25%2B7.05=+32.05m\"\r
\n" ); document.write( "\n" ); document.write( "\"b=+32.05m\"\r
\n" ); document.write( "\n" ); document.write( "now find \"a\"\r
\n" ); document.write( "\n" ); document.write( "one solution\r
\n" ); document.write( "\n" ); document.write( "\"a+=575m%5E2%2F17.95m\"\r
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\n" ); document.write( "\n" ); document.write( "\"a+=32.03m\"\r
\n" ); document.write( "\n" ); document.write( "other solution\r
\n" ); document.write( "\n" ); document.write( "\"a+=575m%5E2%2F32.05m\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=17.94m\"\r
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\n" ); document.write( "\n" ); document.write( "so, dimensions are:\r
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\n" ); document.write( "\n" ); document.write( "\"a+=32.03m\"\r
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\n" ); document.write( "\n" ); document.write( "\"b=+17.95m\"\r
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\n" ); document.write( "\n" ); document.write( "or\r
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\n" ); document.write( "\n" ); document.write( "\"a+=17.94m\"\r
\n" ); document.write( "\n" ); document.write( "\"b=+32.05m\"\r
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\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "\n" ); document.write( "\"100m+=+2%28a%2Bb%29\"\r
\n" ); document.write( "\n" ); document.write( "\"100m+=+2%2832.03m%2B17.94m%29\"\r
\n" ); document.write( "\n" ); document.write( "\"100m+=+2%2849.97m%29\"..round decimal number to nearest whole number\r
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\n" ); document.write( "\n" ); document.write( "\"100m+=+2%2850m%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"100m+=+100m\"\r
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