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the area of a rectangle is 270cm2
\n" ); document.write( "L * w = 270.
\n" ); document.write( " if the shorter side was teduced by 2cm and the longer side was increased by 4 cm. then the area would be increased by 16cm2
\n" ); document.write( "(L+4)*(w-2) = 270 + 16
\n" ); document.write( "FOIL
\n" ); document.write( "Lw - 2L + 4w - 8 = 286
\n" ); document.write( "We can replace Lw with 270
\n" ); document.write( "270 - 2L + 4w - 8 = 286
\n" ); document.write( "-2L + 4w + 262 = 286
\n" ); document.write( "-2L + 4w = 286 - 262
\n" ); document.write( "-2L + 4w = 24
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "-L + 2w = 12
\n" ); document.write( "2w - 12 = L
\n" ); document.write( "In the first equation, replace L with (2w-12)
\n" ); document.write( "(2w-12)*w = 270
\n" ); document.write( "form a quadratic equation
\n" ); document.write( "2w^2 - 12w - 270 = 0
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "w^2 - 6w - 135 = 0
\n" ); document.write( "You can use the quadratic formula, a=1; b=-6; c= -135, but this will factor
\n" ); document.write( "(w - 15)(w + 6) = 0
\n" ); document.write( "two solutions, we want the positive one
\n" ); document.write( "w = 15 cm is the width
\n" ); document.write( "find the length
\n" ); document.write( "270/15 = 18 cm is the length (the original rectangle)
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this by finding the area when length is 22 cm and width is 13 cm
\n" ); document.write( "22 * 13 = 286, which is 16 more than the original area \n" ); document.write( "