<PRE><B>Question 90936</B>
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</PRE>