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Hank observed that the side of one field was 1 KM longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?
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\n" ); document.write( "Assume that the fields are square:
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\n" ); document.write( "Let x = side of the small field:
\n" ); document.write( "Then (x+1) = side of the the medium field
\n" ); document.write( "and (x+3) = side of the largest field
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\n" ); document.write( "Add the areas of the 3 fields
\n" ); document.write( "x^2 + (x+1)^2 + (x+3)^2 = 38
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\n" ); document.write( "FOIL the 2nd * 3rd fields
\n" ); document.write( "x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
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\n" ); document.write( "Remove brackets
\n" ); document.write( "x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
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\n" ); document.write( "Group like terms, subtract 38 from both sides:
\n" ); document.write( "x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
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\n" ); document.write( "3x^2 + 8x - 28 = 0; our old friend the quadratic equation
\n" ); document.write( "Factors to:
\n" ); document.write( "(3x + 14)(x - 2) = 0
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\n" ); document.write( "x = + 2 is the positive solution, ignore the negative solution
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\n" ); document.write( "Small field side = 2 km; Medium = 3Km; Large = 5 km
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\n" ); document.write( "Check it: 2^2 + 3^2 + 5^2 = 38\r
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