Question 417358
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? 

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We are dealing with squares here. 
let x=kilometers of side of smallest square field
 x+1=kilometers of side of one of the larger fields
 x+3=kilometers of side of the largest field

Area of a square=side^2
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=0
3x^2+8x-28=0
factor
(3x+14)(x-2)=0
3x+14=0
3x=-14
x=-14/3 (reject)
x-2=0
x=2
ans:
area of smallest field = x^2=2^2=4 sq km
area of larger field = (x+1)^2=3^2=9 sq km
area of largest field = (x+3)^2=5^2=25 sq km