<PRE><B>Question 205134</B>
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 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?
:
let x = side of the smallest field
then
(x+1) = side of the middle sized field
and
(x+3) = side of the largest field
:
x^2 + (x+1)^2 + (x+3)^2 = 38
FOIL
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
Combine like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 = 38
:
3x^2 + 8x + 10 - 38 = 0
:
3x^2 + 8x - 28 = 0
Factor this to
(3x + 14)(x - 2) = 0
Positive solution
x = 2 km, 2^2 = 4 sq/km, area of the smallest field
and
2 + 1 = 3 km; 3^2 = 9 sq/km; the middle field
and
2 + 3 = 5 km; 5^2 = 25 sq/km; the largest field
:
:
Check solution:
4 + 9 + 25 = 38</PRE>