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 field

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Question 292945: 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?

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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?
:
Let x = length of one side of the smallest field
then
x^2 = the area of the smallest field
:
"the side of one field was 1 kilometer longer than the side of the smallest field"
(x+1) = length of one side of the middle sized field
then
(x+1)^2 = area
:
"the side of the largest field was 3 kilometers longer than the side of the smallest field."
(x+3) = length of one side of the largest field
then
(x+3)^2 = area
:
"the total area of the three fields is 38 square kilometers,"
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
Combine like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
:
3x^2 + 8x - 28 = 0
Factor this to
(3x + 14)(x - 2) = 0
Positive solution
x = 2 km is the side of the smallest field
then
2^2 = 4 sq/km area of the smaller field
:
3^2 = 9 sq/km area of the middle sized field
:
5^2 = 25 sq/km area of the largest field
:
you can see the total will add up to 38 sq/km