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observed that the side of one field was 1 kilometer longer than the side of
\n" ); document.write( " the smallest field and that the side of the largest field was 3 kilometers
\n" ); document.write( " longer than the side of the smallest field. If the total area of the
\n" ); document.write( " three fields is 38 square kilometers, then what is the area of each field.
\n" ); document.write( ":
\n" ); document.write( "let x = side of the smallest square
\n" ); document.write( "area = x^2
\n" ); document.write( ":
\n" ); document.write( "(x+1) = side of the next largest square
\n" ); document.write( "area = (x+1)^2 = (x^2 + 2x + 1)
\n" ); document.write( ":
\n" ); document.write( "(x+3) = side of the largest square
\n" ); document.write( "area = (x+3)^2 = (x^2 + 6x + 9)
\n" ); document.write( ":
\n" ); document.write( "The sum of the three areas:
\n" ); document.write( "x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
\n" ); document.write( "group like terms
\n" ); document.write( "x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
\n" ); document.write( "Combine like terms
\n" ); document.write( "3x^2 + 8x - 28 = 0
\n" ); document.write( "Factors to:
\n" ); document.write( "(3x + 14)(x - 2) = 0
\n" ); document.write( "The positive solution
\n" ); document.write( "x = 2 km side of the smallest field
\n" ); document.write( "then
\n" ); document.write( "2 + 1 = 3 km is the side of the next largest
\n" ); document.write( "and
\n" ); document.write( "2 + 3 = 5 km is the side of the largest field
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\n" ); document.write( "Check solution:
\n" ); document.write( "2^2 + 3^2 + 5^2 =
\n" ); document.write( "4 + 9 + 25 = 38; confirms our solutions \n" ); document.write( "