document.write( "Question 161284: While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest fieldand that the side of the largest fieldwas 3 kilometers longerthan 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? \n" ); document.write( "
Algebra.Com's Answer #118829 by ankor@dixie-net.com(22740)\"\" \"About 
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While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer 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?
\n" ); document.write( ":
\n" ); document.write( "Let x = side of the smallest field
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( "\"the side of one field was 1 kilometer longer than the side of the smallest field\"
\n" ); document.write( "(x+1) = side of this field
\n" ); document.write( ":
\n" ); document.write( "\" the side of the largest field was 3 kilometers longer than the side of the smallest field.\"
\n" ); document.write( "(x+3) = side of the longest field
\n" ); document.write( ":
\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( "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( "x^2 + x^2 + x^2 + 2x + 6x + 1 + 9
\n" ); document.write( "Results:
\n" ); document.write( "3x^2 + 8x + 10 = 38
\n" ); document.write( ":
\n" ); document.write( "3x^2 + 8x + 10 - 38 = 0; subtract 38 from both sides
\n" ); document.write( ":
\n" ); document.write( "3x^2 + 8x - 28 = 0; our old friend the \"quadratic equation\" appears!
\n" ); document.write( "Factor this:
\n" ); document.write( "(3x + 14)(x - 2) = 0
\n" ); document.write( "The positive solution is all we want
\n" ); document.write( "x = +2 km is the side of he smallest
\n" ); document.write( "then
\n" ); document.write( "2+1 = 3 km is the 2nd field
\n" ); document.write( "and
\n" ); document.write( "2+3 = 5 km is the largest field
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution, by finding the total area
\n" ); document.write( "2^2 + 3^ + 5^2 =
\n" ); document.write( "4 + 9 + 25 = 38
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