document.write( "Question 171384: A rectangular pool measures 10m by 5m. A deck, of uniform width, is to be built all the way around the pool such that the total area of the pool and deck will be 126m^2. Set up and solve a quadratic equation to determine the width of the deck. \n" ); document.write( "

Algebra.Com's Answer #126577 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let w=width of the deck
\n" ); document.write( "Area of the pool and deck is:
\n" ); document.write( "(10+2w)(5+2w)=50+30w+4w^2 and we are told that this equals 126m^2, so:
\n" ); document.write( "4w^2+30w+50=126 subtract 126 from each side
\n" ); document.write( "4w^2+30w-76=0 divide each term by 2
\n" ); document.write( "2w^2+15w-38=0---------------quadratic in standard form; solve using quadratic formula:\r
\n" ); document.write( "\n" ); document.write( " $\"w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"w+=+%28-15+%2B-+sqrt%28+225%2B304%29%29%2F%284%29+\"$
\n" ); document.write( " $\"w+=+%28-15+%2B-+%2823%29%29%2F%284%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Neglect negative value for w; widths in this case are positive, so:
\n" ); document.write( " $\"w=8%2F4=2+m\"$ -------------------width of deck\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "(10+4)(5+4)=126
\n" ); document.write( "14*9=126
\n" ); document.write( "126=126\r
\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor\r
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