SOLUTION: I need help please!!! I can't figure this out at all. While finding the amount of seed to plant his three suare wheat fields, Hank observed that the side of one field was 1 kilom

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Question 161327: I need help please!!! I can't figure this out at all.
While finding the amount of seed to plant his three suare 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?
Found 2 solutions by vleith, nerdybill:
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
Find the length of the side on each field.
Let X be the length of the smallest field.
You are told the second field has a side length 1 kilo longer. So its side is (X+1)
You are also told the third field has a side length of (X+3)
The area of a square is given by where s is the length of one side
The total area of all 3 fields is given as 38 Km^2.
All we need to do now is add the three fields and then solve for X

So either or
Thus either or
Since the length cannot be negative, the answer must be 2.
The small field is 2x2, the middle one is 3x3 and the largest one is 5x5.
Is 4 + 9 + 25 = 38?

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
Let x = length of side of smallest field
then because "the side of one field was 1 kilometer longer than the side of the smallest field"
x+1 = length of one field
and because "the largest field was 3 kilometers longer than the side of the smallest field."
x+3 = length of largest field
.
Area of each field is side^2:
x^2 + (x+1)^2 + (x+3)^2 = 38
expanding through FOIL:
x^2 + x^2+2x+1 + x^2+6x+9 = 38
combining like-terms:
3x^2 + 8x + 10 = 38
3x^2 + 8x - 28 = 0
(3x+14)(x-2) = 0
x = {-14/3, 2}
.
We can toss out the negative solution leaving us with:
x = 2 km
x^2 = 4 sq km (smallest field)
.
(x+1)^2 = x^2+2x+1 = 2^2+2(2)+1 = 4+4+1 = 9 sq km (one field)
.
(x+3)^2 = x^2+6x+9 = 2^2+6(2)+9 = 4+12+9 = 25 sq km (largest field)
.
Answer:
4 square kilometers
9 square kilometers
25 square kilometers