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While finding the amount of seed needed to plant his three wheat fields,
\n" ); document.write( " Hank observed that the side of one field was 1 kilometer longer that the side
\n" ); document.write( " of the smallest field and that the side of that the side of the largest field
\n" ); document.write( "was 3 kilometers longer than the side of the smallest field.
\n" ); document.write( "If the total area of the three fields is 38 square kilometers, then what is the area of each field?
\n" ); document.write( ":
\n" ); document.write( "Let x = the side of the smallest field
\n" ); document.write( "then
\n" ); document.write( "(x+1) = side of the middle-sized field
\n" ); document.write( "and
\n" ); document.write( "(x+3) = side of the larger field
\n" ); document.write( ":
\n" ); document.write( "Total of the three areas
\n" ); document.write( "x^2 + (x+1)^2 + (x+3)^2 = 38
\n" ); document.write( "FOIL
\n" ); document.write( "x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
\n" ); document.write( "Combine like terms
\n" ); document.write( "3x^2 + 8x + 10 = 38
\n" ); document.write( ":
\n" ); document.write( "3x^2 + 8x + 10 - 38 = 0
\n" ); document.write( ":
\n" ); document.write( "3x^2 + 8x - 28 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(3x + 14)(x - 2) = 0
\n" ); document.write( "Positive solution
\n" ); document.write( "x = 2 km is the side of the smaller field
\n" ); document.write( "then
\n" ); document.write( "2 + 1 = 3 km is the side of the middle size field
\n" ); document.write( "and
\n" ); document.write( "2 + 3 = 5 km is the side of the large field
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution by finding area of the each field:
\n" ); document.write( "2^2 + 3^2 + 5^2 = 38
\n" ); document.write( "4 + 9 + 25 = 38 \n" ); document.write( "