SOLUTION: This is a word problem. Winter Wheat. 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 long

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Question 140723This question is from textbook Elementary and Intermediate Algebra
: This is a word problem.
Winter Wheat. 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?
We have been using pythagorean theorem in some problems, but I'm not sure how to set this one up. Could you help me with this? Anne This question is from textbook Elementary and Intermediate Algebra

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the area of each field is the side squared

let x="smallest field"

"the side of one field was 1 kilometer longer than the side of the smallest field" __ x+1

"the side of the largest field was 3 kilometers longer than the side of the smallest field" __ x+3

"the total area of the three fields is 38 square kilometers" __ x^2+(x+1)^2+(x+3)^2=38

x^2+x^2+2x+1+x^2+6x+9=38 __ 3x^2+8x+10=38 __ 3x^2+8x-28=0 __ factoring __ (3x+14)(x-2)=0

3x+14=0 __ x=-14/3 __ negative value not realistic

x-2=0 __ x=2