SOLUTION: While finding the amount of seed needed to plant his 3 square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: While finding the amount of seed needed to plant his 3 square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 208038: While finding the amount of seed needed to plant his 3 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 side of the smallest field. If the total area of the 3 fields is 38 square kilometers, then what is the area of each field?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = side of smallest field
x+1= side of second field
x+3 = side of third field

Area = x^2 + (x+1)^2 + (x+3)^2 = 38
x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
3x^2 + 8x +10 = 38

3x^2 + 8x -28=0
(3x+14)(x-2)=0

Two solutions:
3x+14 = 0
3x= -14
x=-14/3 Reject negative answers

x-2=0
x=2
A=4 km^2

x+1=3
A=9 km^2

x+3= 5
A= 25 km^2

Check:
Total area = 4 + 9 + 25= 38 km^2

R^2

Dr. Robert J. Rapalje, Retired