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A field, rectangular in shape, contains 64 square metres;
\n" ); document.write( " if it were 4 metres longer and 3 metres narrower its area
\n" ); document.write( " would be the same.
\n" ); document.write( "Find its dimension.
\n" ); document.write( ":
\n" ); document.write( "let L = original length
\n" ); document.write( "let W = original width
\n" ); document.write( "then
\n" ); document.write( "(L+4) = The \"if\" length
\n" ); document.write( "(W-3) = The \"if\" width
\n" ); document.write( ":
\n" ); document.write( "LW = 64
\n" ); document.write( "and
\n" ); document.write( "(L+4)(W-3) = 64
\n" ); document.write( "FOIL
\n" ); document.write( "LW - 3L + 4W - 12 = 64
\n" ); document.write( "LW - 3L + 4W - 12 - 64 = 0
\n" ); document.write( "LW - 3L + 4W - 76 = 0
\n" ); document.write( "Replace LW with 64
\n" ); document.write( "64 - 3L + 4W - 76 = 0
\n" ); document.write( "We have
\n" ); document.write( "4W - 3L - 12 = 0
\n" ); document.write( "4W = 3L + 12
\n" ); document.write( "divide by 4
\n" ); document.write( "W = .75L + 3
\n" ); document.write( "then replacing W in the original area equation (L*W)
\n" ); document.write( "L*(.75L+3) = 64
\n" ); document.write( "A quadratic equation
\n" ); document.write( ".75L^2 + 3L - 64 = 0
\n" ); document.write( "Solve for L using the quadratic formula: a=.75; b=3; c=-64
\n" ); document.write( "The positive solution ~ 7.45 is the length
\n" ); document.write( ":
\n" ); document.write( "Find the width:
\n" ); document.write( ":
\n" ); document.write( "See if that checks out
\n" ); document.write( "(7.45+4)*(8.6-3) ~ 64
\n" ); document.write( ":
\n" ); document.write( "The dimensions are not exact: L ~ 7.45; W ~ 8.6; is close \n" ); document.write( "