Question 292945
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