# SOLUTION: 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

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 Question 205134This question is from textbook Elementary and Intermediate Algebra : 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? This question is from textbook Elementary and Intermediate Algebra Answer by ankor@dixie-net.com(15645)   (Show Source): You can put this solution on YOUR website!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? : let x = side of the smallest field then (x+1) = side of the middle sized field and (x+3) = side of the largest field : x^2 + (x+1)^2 + (x+3)^2 = 38 FOIL x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38 Combine like terms x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 = 38 : 3x^2 + 8x + 10 - 38 = 0 : 3x^2 + 8x - 28 = 0 Factor this to (3x + 14)(x - 2) = 0 Positive solution x = 2 km, 2^2 = 4 sq/km, area of the smallest field and 2 + 1 = 3 km; 3^2 = 9 sq/km; the middle field and 2 + 3 = 5 km; 5^2 = 25 sq/km; the largest field : : Check solution: 4 + 9 + 25 = 38