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
![](Algebra-Quadratic-Equation-Id21_files/image004.png)
The total area is
![](Algebra-Quadratic-Equation-Id21_files/image006.png)
This implies that
![](Algebra-Quadratic-Equation-Id21_files/image008.png)
which has two solutions
![](Algebra-Quadratic-Equation-Id21_files/image010.png)
but one of the solutions is negative, so we disregard it. Therefore,
![](Algebra-Quadratic-Equation-Id21_files/image012.png)
![](Algebra-Quadratic-Equation-Id21_files/image014.png)