<PRE><B>Question 200549</B>
 Hank observed that:
the side of one field was 1 kilometer longer than the side of the smallest field
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?
:
The sides of the 3 fields
x = smallest field side
(x+1) = medium field side
(x+3) = largest field side
:
Area equation:
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
remove brackets, combine like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
Results in a quadratic equation
3x^2 + 8x - 28 = 0
Factors to:
(3x + 14)(x - 2) = 0
Positive solution:
x = 2 km is the side of the small field
Area: 2^2 = 4 sq/km
then
2 + 1 = 3 km is the side of the medium field
Area: 3^2 = 9 sq/km
and
2 + 3 = 5 km is the side of the large field
Area: 5^2 = 25 sq/km
;
;
Check solution: 4 + 9 + 25 = 38</PRE>