Question 58655
Hank observed that the side of one field was 1 KM 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? 
:
Assume that the fields are square:
:
Let x = side of the small field:
Then (x+1) = side of the the medium field
and (x+3) = side of the largest field
:
Add the areas of the 3 fields
x^2 + (x+1)^2 + (x+3)^2 = 38
:
FOIL the 2nd * 3rd fields
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
:
Remove brackets
x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
:
Group like terms, subtract 38 from both sides:
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
:
3x^2 + 8x - 28 = 0; our old friend the quadratic equation
Factors to:
(3x + 14)(x - 2) = 0
:
x = + 2 is the positive solution, ignore the negative solution
:
Small field side = 2 km; Medium = 3Km; Large = 5 km
:
Check it: 2^2 + 3^2 + 5^2 = 38