Question 162784This question is from textbook Elementary and Intermediate
: 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 threes fields is 38 square kilometers, then what is the area of each field?
This question is from textbook Elementary and Intermediate
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let s = side of smallest field.
let m = side of middle field.
let l = side of largest field.
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s = s kilometers
m = s+1 kilometers
l = s+3 kilometers
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total area of all 3 fields is 38 square kilometers.
s^2 + m^2 + l^2 = 38
since m = s+1 and l = s+3, substitute in equation to get
s^2 + (s+1)^2 + (s+3)^2 = 38
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this becomes
s^2
+ s^2 + 2s + 1
+ s^2 + 6s + 9
= 38
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this becomes
3s^2 + 8s + 10 = 38
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subtracting 38 from both sides of equation and it becomes
3s^2 + 8s - 28 = 0
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factoring this equation yields
(3s+14) * (s-2) = 0
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s = 2 was substituted in original equation of s^2 + (s+1)^2 + (s+3)^2 = 38 and is good.
s = -14/3 was rejected because the side of the field can't be negative. it was substituted in the original equation and it worked, but it can't be used.
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smallest field is 2 kilometers per side.
middle field is 3 kilometers per side.
largest field is 5 kilometers per side
2^2 + 3^2 + 5^2 = 4 + 9 + 25 = 38 square kilometers.
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equation is satisfied.
area of the smallest field is 4.
area of the middle field is 9.
area of the largest field is 25.
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