Question 214813: While finding the amount of seed needed to plant his three wheat fields, Hank observed that the side of one field was 1 kilometer longer that 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 kilomters, then what is the area of each field?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! While finding the amount of seed needed to plant his three wheat fields,
Hank observed that the side of one field was 1 kilometer longer that the side
of the smallest field and that the side of 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?
:
Let x = the side of the smallest field
then
(x+1) = side of the middle-sized field
and
(x+3) = side of the larger field
:
Total of the three areas
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
Combine like terms
3x^2 + 8x + 10 = 38
:
3x^2 + 8x + 10 - 38 = 0
:
3x^2 + 8x - 28 = 0
Factors to
(3x + 14)(x - 2) = 0
Positive solution
x = 2 km is the side of the smaller field
then
2 + 1 = 3 km is the side of the middle size field
and
2 + 3 = 5 km is the side of the large field
:
:
Check solution by finding area of the each field:
2^2 + 3^2 + 5^2 = 38
4 + 9 + 25 = 38
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