document.write( "Question 518189: A swimming pool 6 m wide and 10 m long is to be surrounded by a cement path of uniform width. The area of the path is equal to the area of the pool. What is the width of the path? \n" ); document.write( "

Algebra.Com's Answer #345086 by josmiceli(19441) $\"\"$ $\"About$

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the area of the pool is
\n" ); document.write( " $\"+6%2A10+=+60+\"$ m2
\n" ); document.write( "Let $\"x\"$ = the width of the path
\n" ); document.write( "Both the length and width are increased by $\"2x\"$
\n" ); document.write( "The area of the path + pool = $\"+120+\"$ m2
\n" ); document.write( " $\"+%286+%2B+2x%29%2A%2810+%2B+2x%29+=+120+\"$
\n" ); document.write( " $\"+60+%2B+20x+%2B+12x+%2B+4x%5E2+=+120+\"$
\n" ); document.write( " $\"+4x%5E2+%2B+32x+=+60+\"$
\n" ); document.write( " $\"+x%5E2+%2B+8x+=+15+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( "

\n" ); document.write( " $\"+%28+x+%2B+4%29%5E2+=+31+\"$
\n" ); document.write( " $\"+x+%2B+4+=+sqrt%2831%29+\"$
\n" ); document.write( " $\"+x+=+sqrt%2831%29+-+4+\"$
\n" ); document.write( " $\"+x+=+5.5678+-+4+\"$
\n" ); document.write( " $\"+x+=+1.5678+\"$
\n" ); document.write( "The width of the path is 1.5678 m
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+%286+%2B+2x%29%2A%2810+%2B+2x%29+=+120+\"$
\n" ); document.write( " $\"+%286+%2B+2%2A1.5678%29%2A%2810+%2B+2%2A1.5678%29+=+120+\"$
\n" ); document.write( " $\"+%286+%2B+3.1356%29%2A%2810+%2B+3.1356%29+=+120+\"$
\n" ); document.write( " $\"+9.1356%2A13.1356+=+120+\"$
\n" ); document.write( " $\"+120.0016+=+120+\"$
\n" ); document.write( "close enough \n" ); document.write( "

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