document.write( "Question 747317: rectangle with perimeter 20cm
\n" ); document.write( "length xcm
\n" ); document.write( "diagonal 8cm\r
\n" ); document.write( "\n" ); document.write( "show x^2 - 10x +18 = 0 \n" ); document.write( "

Algebra.Com's Answer #454892 by MathLover1(20855) $\"\"$ $\"About$

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\n" ); document.write( "rectangle with perimeter $\"2x%2B2%2AW=20cm\"$ where $\"W\"$ is the width and
\n" ); document.write( " $\"x\"$ is the length\r
\n" ); document.write( "\n" ); document.write( "if diagonal $\"d=8cm\"$ then $\"d%5E2=W%5E2%2Bx%5E2\"$ => $\"64cm%5E2=W%5E2%2Bx%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2x%2B2%2AW=20cm\"$ ..eq.1...solve for $\"x\"$ ..divide all terms by $\"2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%2BW=10cm\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=10cm-W\"$ .....plug in $\"64cm%5E2=W%5E2%2Bx%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"64cm%5E2=W%5E2%2B%2810cm-W%29%5E2\"$ ......solve for $\"W\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"64cm%5E2=W%5E2%2B100cm%5E2-20W%2BW%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2W%5E2-20W%2B100cm%5E2-64cm%5E2=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2W%5E2-20W%2B36cm%5E2=0\"$ .....divide all terms by $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W%5E2-10W%2B18cm%5E2=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A18+%29%29%2F%282%2A1%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2810+%2B-+sqrt%28100-72+%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2810+%2B-+sqrt%2828%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2810+%2B-+sqrt%284%2A7%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=+%2810+%2B-+2sqrt%287%29%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"W+=5+%2B-+sqrt%287%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"W+=5+%2B+sqrt%287%29=7.65cm+\"$ or $\"W+=5+%2B+sqrt%287%29=2.35cm+\"$ \r
\n" ); document.write( "\n" ); document.write( "now find $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=10cm-W\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=10cm-7.65cm=2.35cm\"$ or $\"x=10cm-2.35cm=7.65cm\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, we will take the length $\"highlight%28x=7.65cm%29\"$ and the width $\"highlight%28W+=2.35cm%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now show $\"x%5E2+-+10x+%2B18+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%287.65%29%5E2+-+10%2A7.65+%2B18+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"58.5225+-+76.5+%2B18+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"58.5%2B18+-+76.5+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"76.5+-+76.5+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=+0\"$
\n" ); document.write( " \n" ); document.write( "

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