document.write( "Question 788273: one hundred tiles on certain size were used to pave a floor, if a tile which measures 4cm less on each side will be used, 225 tiles will be needed, find the size of the larger tile. \n" ); document.write( "
Algebra.Com's Answer #478476 by ankor@dixie-net.com(22740)\"\" \"About 
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one hundred tiles on certain size were used to pave a floor, if a tile which measures 4cm less on each side will be used, 225 tiles will be needed, find the size of the larger tile.
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\n" ); document.write( "Let x = side of the larger tile
\n" ); document.write( "then
\n" ); document.write( "x^2 = area of the larger tile
\n" ); document.write( "and
\n" ); document.write( "(x-4)^2 = area of the smaller tile
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\n" ); document.write( "225(x-4)^2 = 100x^2
\n" ); document.write( ":
\n" ); document.write( "225(x^2-8x+16) = 100x^2
\n" ); document.write( ":
\n" ); document.write( "225x^2 - 1800x + 3600 = 100x^2
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\n" ); document.write( "225x^2 - 100x^2 - 1800x + 3600 = 0
\n" ); document.write( ":
\n" ); document.write( "125x^2 - 1800x + 3600 = 0
\n" ); document.write( "Simplify, divide by 25
\n" ); document.write( "5x^2 - 72x + 144 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(5x-12)(x-12)
\n" ); document.write( "Reasonable solution
\n" ); document.write( "x = 12 cm is the side of the larger tile
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\n" ); document.write( "Check this by finding the area by each, should be the same
\n" ); document.write( "100*12^2 = 14400 sq/cm
\n" ); document.write( "225*8^2 = 14400 sq/cm \n" ); document.write( "
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