SOLUTION: 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 s

Algebra ->  Rectangles -> SOLUTION: 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 s      Log On


   

Question 90936: 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 three fields is 38 square kilometers, then what is the area of each field?
Answer by ankor@dixie-net.com(22740) About Me  (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 = side of the smallest
Then
(x+1) = side of the medium field
Then
(x+3) = side of the largest
:
x^2 + (x+1)^2 + (x+3)^2 = 38
:
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
:
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
:
3x^2 + 8x - 28 = 0
:
(3x + 14)(x - 2) = 0
:
x = +2 km is the side of the smallest field
:
2^2 = 4 sq/km area of the smaller field
:
3^2 = 9 sq/km area of the medium field
:
5^2 = 25 sq/km area of the largest field
:
:
Check: 4 + 9 + 25 = 38