Question

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 smallest field. If the total area of the three fields is 38 square kilometers, than what is the area of each field?

Answer 1

x^2 + (x+1)^2 + (x+3)^2 = 38

expand, simplify, then solve the quadratic equation.

reject one of the answers which will be negative.

Answer 2

s = side of smallest field
(s+1) = side of middle fiels
(s+3) = side of biggest fiels
so
s^2 + (s+1)^2 + (s+3)^2 - 38 = 0

s^2 + s^2 + 2 s + 1 + s^2 +6 s + 9 - 38 = 0

3 s^2 + 8 s - 28 = 0

(3s+14)(s-2) = 0
s = 2 is positive answer
area of small field = 4
then
s+1 = 3
area of middle size field = 9
s+3 = 5
area of big field = 25