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 fie
Question 280766: 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? Found 2 solutions by richwmiller, oberobic:Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website! Each field is square, so their areas are simply l*w = l^2 = w^2.
.
x = sides of square field 1
y = sides of square field 2
z = sides of square field 3
.
x^2 + y^2 + z^2 = 38 :: the sum of the areas of the three fields is 38
.
x = sides of the smallest field
y = x+1 = sides of the middle-sized field
z = x+3 = sides of the largest field
.
x^2 + (x+1)^2 + (x+3)^2 = 38
.
x^2 + (x^2 +2x +1) + (x^2 +6x +9) = 38
.
collecting terms and simplifying
.
3x^2 + 8x + 10 - 38 = 0
3x^2 + 8x -28 = 0
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factoring
(3x +14 )(x - 2) = 0
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The roots are x=-14/3 and x=2.
Negative values are the sides of fields are nonsensical, so we suspect x=2.
.
x = 2
y = x+1 = 3
z = x+3 = 5
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Checking the proposed solution...
.
Does x^2 +y^2 +z^2 = 38?
2^2 = 4
3^2 = 9
5^2 = 25
4+9+25 = 38
YES!
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Answer: The areas of each of the three square fields are: 4, 9, and 25.
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Done
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