document.write( "Question 202753This question is from textbook
\n" ); document.write( ": Winter wheat. While finding the amount of seed needed
\n" ); document.write( "to plant his three square wheat fields, Hank observed that
\n" ); document.write( "the side of one field was 1 kilometer longer than the side
\n" ); document.write( "of the smallest field and 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,
\n" ); document.write( "then what is the area of each field? \n" ); document.write( "

Algebra.Com's Answer #152929 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let x = the side of the smaller field, then (x+1) = the side of the middle field and (x+3) equal the side of the largest field.
\n" ); document.write( "The three areas, which sum to 38 sq.km. are:
\n" ); document.write( " $\"x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B3%29%5E2++=+38\"$ Simplify.
\n" ); document.write( " $\"x%5E2%2B%28x%5E2%2B2x%2B1%29%2B%28x%5E2%2B6x%2B9%29+=+38\"$
\n" ); document.write( " $\"3x%5E2%2B8x%2B10+=+38\"$ Subtract 38 from both sides.
\n" ); document.write( " $\"3x%5E2%2B8x-28+=+0\"$ Factor this trinomial.
\n" ); document.write( " $\"%283x%2B14%29%28x-2%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"3x%2B14+=+0\"$ or $\"x-2+=+0\"$
\n" ); document.write( " $\"3x+=+-14\"$ or $\"x+=+2\"$ Discard the negative solution as the side must be a positive value.
\n" ); document.write( " $\"highlight%28x+=+2%29\"$
\n" ); document.write( "The area of the smallest field is $\"x%5E2+=+4\"$ sq.km.
\n" ); document.write( "The area of the middle field is $\"%28+x%2B1%29%5E2+=+9\"$ sq.km.
\n" ); document.write( "The area of the largest field is $\"%28x%2B3%29%5E2+=+25\"$ sq.km.
\n" ); document.write( " $\"4%2B9%2B25+=+38\"$ \n" ); document.write( "

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