document.write( "Question 514864: A 10m by 20m pool is surrounded by a deck of uniform width. The area of the deck is 216m^2. How wide is the deck? \n" ); document.write( "
Algebra.Com's Answer #343610 by drcole(72)\"\" \"About 
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Try drawing a picture. Let x represent the width of the deck. We can break the deck up into eight pieces: the two rectangles adjacent to the long sides of the pool, the two rectangles adjacent to the short sides of the pool, and the four corners, each of which is a square with sides the width of the deck. Let's describe the areas of each piece of the deck algebraically:\r
\n" ); document.write( "\n" ); document.write( "Each rectangle adjacent to a long side of the pool has length 20 meters and width x meters, and thus area 20x square meters.\r
\n" ); document.write( "\n" ); document.write( "Each rectangle adjacent to a short side of the pool has length 10 meters and width x meters, and thus area 10x square meters.\r
\n" ); document.write( "\n" ); document.write( "Each square corner has all sides of width x meters, and thus has area x^2 square meters.\r
\n" ); document.write( "\n" ); document.write( "Since there are two of each rectangle and four square corners, the total area of the deck is:\r
\n" ); document.write( "\n" ); document.write( "\"+2%2820x%29+%2B+2%2810x%29+%2B+4x%5E2+\"\r
\n" ); document.write( "\n" ); document.write( "We know that the area of the deck is 216 square meters, so we have a quadratic equation we can solve:\r
\n" ); document.write( "\n" ); document.write( "\"+2%2820x%29+%2B+2%2810x%29+%2B+4x%5E2+=+216+\"\r
\n" ); document.write( "\n" ); document.write( "Now we solve:\r
\n" ); document.write( "\n" ); document.write( "\"+40x+%2B+20x+%2B+4x%5E2+=+216+\" (simplify the left hand side)
\n" ); document.write( "\"+60x+%2B+4x%5E2+=+216+\" (combine like terms)
\n" ); document.write( "\"+4x%5E2+%2B+60x+-+216+=+0+\" (subtract 216 from both sides and rearrange terms)
\n" ); document.write( "\"+x%5E2+%2B+15x+-+54+=+0+\" (divide both sides by 4)
\n" ); document.write( "\"+%28x+%2B+18%29%28x+-+3%29+=+0+\" (factor the quadratic: 18 and -3 have a sum of 15 and a product of -54)\r
\n" ); document.write( "\n" ); document.write( "Setting both factors equal to 0, we get the roots x = -18 and x = 3. Now x = -18 cannot be the solution, since x represents a width and cannot be negative. So the only realistic solution is x = 3. So the deck has a uniform width of 3 meters. \n" ); document.write( "
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