Problem: 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 size 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 is 38 square kilometers, then what is the area of each field?
Solution: Let
be the sides of the fields. We know that
The total area is
This implies that
which has two solutions
but one of the solutions is negative, so we disregard it. Therefore,
