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?
please help...im confused with word problems
Answer by lwsshak3(11628)   (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?
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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
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